This Essay should be read in
conjunction with EssaysFourand Eight Parts
One,Two
and Three.

For some reason I can't
work out, Internet Explorer 11 will no longer play the videos I have posted to
this page. Certainly not on my computer! However, as far as I can tell, they
play in other Browsers.

If you are using Internet Explorer 10
(or later), you might find some of the links I have used won't work properly
unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select
'Compatibility View Settings' and then add this site (anti-dialectics.co.uk). I have as yet no idea how
Microsoft's new browser,
Edge, will handle these
links.

Moreover,
if you are viewing this with Mozilla Firefox, you might not be able to read all
the symbols I have used --
Mozilla often replaces them with a "°". I do not know if other browsers are similarly affected.

~~~~~~oOo~~~~~~

As is the case with all my Essays, nothing here should be read as an attack
either on Historical Materialism [HM] -- a theory I fully accept --, or,
indeed,
on revolutionary socialism. I remain as committed to the self-emancipation of the
working class and the dictatorship of the proletariat as I was when I first became a revolutionary
nearly thirty years ago.

The
difference between Dialectical
Materialism [DM] and HM, as I see it, is explained
here.

It
is also worth pointing out thatphrases like "ruling-class theory", "ruling-class view of reality",
"ruling-class ideology" (etc.) used at this site (in connection with
Traditional Philosophy and DM), aren't meant to
suggest that all or even most members of various ruling-classes
actually invented these ways of thinking or of
seeing the world (although some of them did -- for example,
Heraclitus,
Plato,
Cicero,and
Marcus Aurelius).
They are intended to
highlight theories (or "ruling ideas") that are conducive to, or which rationalise the
interests of the various ruling-classes history has inflicted on humanity, whoever invents them.
Up until
recently this dogmatic approach to knowledge had almost invariably been promoted by thinkers who
either relied on ruling-class patronage, or who, in one capacity or another, helped run
the system
for the elite.**

However, that will become the
central topic of Parts Two and Three of Essay Twelve (when they are published); until then, the reader is
directed
here,
here, and
here for
more
details.

[**Exactly
how this applies to DM will, of course, be explained in the other Essays
published at this site (especially
here,
here,
and here).
In addition to the three links in the previous paragraph, I have summarised the
argument (but this time aimed at absolute beginners!)
here.]

It is also worth pointing out that a good 50% of my case
against DM has been relegated to the
End Notes.
Indeed, in this particular Essay, most of the supporting evidence and
argument is to
be found there. This
has been done to allow the main body of the Essay to flow a little more
smoothly. In many cases, I have added numerous qualifications, clarifications,
and considerably more detail to what I have to say in the main body. In
addition, I have raised several objections (some obvious, many not -- and some
that will have occurred to the reader) to my own arguments -- which I have then
answered.
[I explain why I have adopted this tactic in
Essay One.]

If readers skip this
material, then my answers to any qualms or objections readers might have will be
missed, as will my expanded comments and clarifications.

[Since I have been
debating this theory with comrades for over 25 years, I have heard all the
objections there are! Many of the more recent on-line debates are listed here.]

Update 07/03/2014: I have just received a copy of
Burger et al (1980), the existence of which I had been unaware until a
few weeks ago. One of the contributors to this book, Hyman Cohen [Cohen
(1980)] seems to have anticipated (and answered) one or two of the points
I have raised in this Essay. Unfortunately, Cohen's 'answers' also fail miserably; I
will attempt to explain why that is so in a future re-write of this Essay.

Update
29/11/2016: I have now added a few thoughts about Cohen's egregious logical confusions
to Essay Four
Part One.

Finally, anyone puzzled by the
unremittingly hostile tone I have adopted toward DM/'Materialist Dialectics'
[MD] in these Essays might do well to read
this first.

As of October 2017, this Essay is just
under 86,000 words long; a
much shorter summary
of some of its main ideas can be found
here,
and a more recent summary,
here.

The
material presented below does not represent my final view of any of the
issues raised; it is merely 'work in progress'.

Anyone using these links must remember that
they will be skipping past supporting argument and evidence set out in earlier
sections.

If your Firewall/Browser has a pop-up blocker, you will need to press the
"Ctrl" key at the same time or these and the other links here won't work!

I have adjusted the
font size used at this site to ensure that even those with impaired
vision can read what I have to say. However, if the text is still either too
big or too small for you, please adjust your browser settings!

DM-theorists
in general attempt to illustrate the 'contradictory' nature of reality by appealing to a
handful of examples, some of
which are based on a variation of one of
Zeno's Paradoxes. For instance, in order to
highlight the limitations of
FL, Engels
directed our attention to the 'contradictory' nature of motion, depicting it in
the following way:2

"[S]o long as we consider things as at rest and
lifeless, each one by itself, alongside and after each other, we do not run up
against any contradictions in them. We find certain qualities which are partly
common to, partly different from, and even contradictory to each other, but
which in the last-mentioned case are distributed among different objects and
therefore contain no contradiction within. Inside the limits of this sphere of
observation we can get along on the basis of the usual, metaphysical mode of
thought. But the position is quite different as soon as we consider things in
their motion, their change, their life, their reciprocal influence on one
another. Then we immediately become involved in contradictions. Motion itself is
a contradiction: even simple mechanical change of position can only come about
through a body being at one and the same moment of time both in one place and in
another place, being in one and the same place and also not in it. And the
continuous origination and simultaneous solution of this contradiction is
precisely what motion is." [Engels (1976), p.152.]3

As is well-known,
Engels borrowed the above ideas
from Hegel.
In this passage he connects change with motion, and then both with
"contradictions"
that supposedly exist in nature and society (which he does elsewhere in the same book).

However,
before this passage is examined in detail, there
are several problems it presents which will need to addressed first since they influence the
overall interpretation placed on the conclusions Engels
seems to have reached.
Indeed, left unresolved they threaten to undermine
completely what he had to say about motion and change.

"Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Ibid.
Bold emphasis added.]

Exactly
who is supposed to do the
"asserting" and who the "solving", here?
It could
be argued that these words were meant to be taken metaphorically. But, if
that
is so, what is the force of Engels's
use of "precisely"?

Even more to the point: if Engels was
speaking figuratively what has "assertion and simultaneous solution" got to do
with motion? This isn't even a good
metaphor!

Perhaps Engels intended to say that these phrases merely pertain
to the
description
of motion? In that case, his conclusions will be limited to language
about motion, not 'motion itself'.4

How
exactly are contradictions "solved"? Are they like puzzles, riddles and
mysteries? If they are, do they disappear once they have been "solved"? Puzzles
and mysteries cease to be puzzles or mysteries when they have been resolved. Is
this the same with these contradictions?4a
If so, do new contradictions immediately take
their place? In which case, is each "solved" contradiction replaced by the 'same'
contradiction further along the path of that moving body -- or by an entirely new one?
But, how
might any of this be confirmed? And, how do we know if there is only one contradiction present,
or countless thousands for each unit of time involved? If there is more than
one contradiction, how are they all connected with any given body in motion? Does each contradiction arise and fall as that body moves?
Or is there a single, extended contradiction spread
out, as it were, right along its entire trajectory? Is this 'extended contradiction'
then
perhaps
this: that a moving body is "here and
not here, in general",
so to speak?

More puzzling still: Are these contradictions "solved" by some mind or other
comprehending them first? If not, what sense can be given to the word "solved"? And, what precisely is there
to understand in a contradiction so that a 'solution' is required
in the first place, but which now mysteriously still helps further propel the moving object
along (if it does)? On the other hand, if a 'solution' is required, how was
this done before human beings evolved?

At first sight,
Engels appears
to be arguing that it is only our understanding of motion that is
contradictory:

This might help explain why the passage refers to the "continual
assertion" of contradictions, since it is evident that only human beings can assert
anything. If so, it looks like Engels thought that human observers can't avoid "asserting" such contradictions whenever they attempt to describe
motion, and that might itself be a consequence of their partial understanding of the
'absolute truth' about motion. On the
other hand, this
conundrum could be a fault of logic, or even of language, both of which aresaid by some to be
inadequate to the task. But, that would fail to explain how and why
contradictions, upon being "asserted", are immediately "solved" and then
promptly re-"asserted".

Anyway, and worse, this would appear to mean that it is only human
understanding of motion that is contradictory, not 'reality itself'
that is --
unless, of course, we are to suppose that nature is Mind. Or, maybe it means that
it is the 'self-development of Mind' that propels bodies along? But, the former
alternative suggests that when reality isfully understood all such contradictions should disappear. If so, this in turn implies
that motion might one day cease, all contradictions having been 'solved'! Indeed, if
contradictions actually 'cause' motion, then their complete resolution should, it
seems, freeze nature in its entirety.Or, is it
that motion will just stop being (orappearing to be) contradictory, but will otherwise
carry on as normal? Or, does it
mean that nature will just slow down as it is better understood (i.e., if
what we know about motion and change becomes less and less contradictory)? Who
can say? Certainly, in the 140 years since Engels wrote these enigmatic words, DM-fans
have been more content merely to repeat them than they have been concerned to
raise, let alone consider, these
glaringly obvious questions.

Admittedly, DM-theorists
distinguish between subjective and objective dialectics -- the
former relating to our (perhaps decreasingly) partial grasp of the 'nature of
reality', the latter referring to processes in the 'objective world' independent
of our will or our knowledge. Even so, it is still
unclear how this helps answer the above questions. If the human mind "solves" the
contradictions involved in motion, wouldn't this mean that things
actually stop moving?
Wouldn't
it also indicate that movement only seems to be contradictory because
of the partial nature of human knowledge -- implying that motion isn't really
contradictory?Plainly,that is because these 'subjective contradictions' ought to disappear
as knowledge grows, which in turn means that (in the limit) reality isn't
'contradictory', after all. In that case, it is only our 'one-sided knowledge' of nature
that fools us into concluding otherwise!

Well, perhaps this suggests that we don't really understand these
'contradictions' to begin with.
But, then again, that would fail to explain why contradictions are promptly
reasserted upon being "solved"; nor is it at all clear how they could
be "solved" if no one understands
them, or if no one understands nature fully. More alarmingly, this might mean that the
objects in question aren't
really moving,
as Zeno originally contended!

This appears to confirm the conclusion
that motion isn't really a 'contradictory-in-itself' -- that is, that it is simply our
'one-sided' perspective that misleads us into concluding otherwise. After all, Engels tells us that
the "continual assertion" and "solution" of this contradiction is "precisely what motion
is". Why then does Engels say that this reveals "precisely" what motion is, as opposed to arguing that
it merely depicts what we subjectively think it is?

An appeal
to "objective dialectics" can't help us comprehend what Engels means
here, either, since neither assertions nor solutions occur in nature
(apart, that is, from the intelligent beings who make or who provide them). And, if
that is so, these non-objective assertions and solutions can't
have been reflected
in the mind of observers as part of an objective scientific theory -- or, indeed, as part
of 'objective dialectics'. If
assertions and solutions don't exist in the world
independent of the individuals who make/invent them, there would be nothing
there in the material world
for the minds of scientists or dialecticians to reflect.

And if that is
so, what has assertion and solution got to do with motion in the
real world? And why did Engels think they were at all relevant?

"Motion itself is a contradiction; even simple mechanical change of place can
only come about through a body being both in one place and in another place
at one and the same moment of time, being in one and the same place and also not
in it. And the continual assertion and simultaneous solution of this
contradiction is precisely what motion is." [Ibid.
Bold emphasis added.]

More
specifically, in relation to moving bodies, it is pertinent to ask:
How far apart are the two
proposed "places" that a moving object is supposed to occupy while at
the same time not occupying one of them?
Is there a minimum distance
involved?
The answer can't be "It doesn't matter; any distance will do." That is because,
as we will see,
if a moving object is in two places at once, then it can't truly be said to be in
the first of these before it is in the second -- since it is in both
of them at
the same time. So, unless great care is taken
specifying how far apart these "two places" are, the DM-view of motion would have,
say, an aeroplane landing at the same time as it took off! If any distance will do,
then the distance between the two airports involved is as good as any other. [I
return to this topic and discuss it in much more detail
later in this Essay.]

Indifference
here, in this respect, would have you arriving at your
destination at the same time as you left home!

Anyway, whatever the answer to that annoying conundrum happens to
be -- as is well known
-- between any two locations there is a potentially infinite
number of intermediary points (that is, unless
we are prepared to impose an a priori limitation on nature by denying this).

Does a
moving body, therefore, (i) occupy all of these
intermediate points at once? Or,
(ii) does it occupy each pair of points successively?

If the former is the case, does this imply that a moving object can be in an infinite number
of places
at the same time,
and not just in two, as Engels asserted? On the other hand, if Engels is correct,
and a moving body only occupies (at most) two places at once, wouldn't that suggest that motion isdiscontinuous? That is because such an account seems to picture
motion as a peculiar stop-go sort of affair, since a moving body would have to skip past
(but not occupy, somehow?) the potentially infinite number of intermediary
locations between any two arbitrary points (the second of which it then occupies), if it is restricted to being in
at most two of them at any one time, and is therefore stationary at
the second of these two points. If a moving body occupies exactly two
points at once, it must be stationary in the second of those two. On the
other hand, if it is still moving in the second of these two locations then it
must also occupy a third place at the same time, otherwise it would be
stationary there (if we accept what Engels says about motion). The "at most two"
qualifier ruled that option out. But, that itself appears to run
contrary to the hypothesis that motion is continuous and therefore
contradictory -- or, it
runs counter to that hypothesis in any straight-forward sense, at the very least. It is surely the continuous
nature of motion that poses problems for a logic (i.e.,
FL) -- which is allegedly built on
a static,
discontinuous view of reality, this being the picture that
traditional
logic is supposed to
work with
--,
or, so we have been told by generations of dialecticians. [We will return to
this knotty problem and consider it in much more detail
below.]

It could be argued that no matter how much we
'magnify' the path of a moving body, it will still occupy two points at
once, being in one of them and not in it at the same time. And yet, that doesn't solve
the problem, for if there is indeed a potentially infinite number of intermediary
points between any two locations, a moving body must occupy more than two of
them at
once, contrary to what Engels said:

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Ibid.
Bold emphasis added.]

Hence, between any two points, P and Q
-- located at, say, (Xp, Yp, Zp)
and (Xq, Yq, Zq),
respectively--
that
a moving object, M, occupies (at the same
"moment in time", T1),
there are, for example, the following intermediary points: (X1, Y1, Z1),
(X2, Y2, Z2), (X3, Y3, Z3),...,
(Xi, Yi,
Zi),..., (Xn, Yn, Zn)
-- where n itself can be arbitrarily large.
Moreover, the same applies to (X1, Y1, Z1)
and (X2, Y2, Z2):
there is a potentially infinite number of intermediate points between these two, and so on.

So, if Engels is right, M must occupy not
just P and Q at the same instant, it must occupy all these
intermediary points, as well -- again, all at T1.
That can only mean that M is located in a potentially infinite number of
places, all at the same "moment". It must therefore not only be in and not inP at T1,
it must be in and not in each of (X1, Y1, Z1),
(X2, Y2, Z2), (X3, Y3, Z3),...,
(Xi, Yi,
Zi),...,and (Xn, Yn, Zn)
at T1,
just as it must be in all the intermediary points between (X1, Y1, Z1)
and (X2, Y2, Z2),
if it is also to be in Q at the same "moment".

And, what is worse: M must move
through (or be in) all these intermediate pointswithout time having advanced one instant!

That is, M will have achieved all this in zero seconds!

M must therefore be moving with an
infinite velocitybetweenP and Q!

Unless, of course, we decide to re-define
"velocity" so that it is no longer the expression of a functional link between
distance and time -- calculated by dividing the former by the latter.

But, if not, what then is it?

[An appeal to the
Calculus
here -- or, rather, to a DM-interpretation of the Calculus -- would be to
no avail, as we will see in Essay Seven
Part One. See also
this sub-section
of the present Essay.]

Of course, we could always claim that by "same
moment" Engels meant "same temporal interval", but as we will also see, this
reply would scupper his theory even faster. [No pun intended.] That is because, if by "same
moment" Engels meant "same temporal interval", then there is no reason why "same
point" can't also mean "same spatial interval", at which point the alleged
'contradiction' simply vanishes. [Again, no pun intended!]

[Why that is so will be explained
below. Indeed, we
will also
see that this alternative (i.e., that a moving body occupies all the
intermediate points between any two points, all at the same time) poses even
more
serious problems for Engels's
theory than this --, that is, over and above implying that 'dialectical' objects move with infinite velocities.]

However, if M moves from P to Q
in temporal interval, T, comprised of sub-intervals, T1, T2, T3,
..., Tn,
each of which is also comprised of its own sub-intervals, then M will be
located at P at T1
and then at Q at Tn,
which will, of course, mean that M won't be in these two places at the
same time, although it will be located at these two points in the same
temporal interval. The 'contradiction' Engels claims to see here has now vanished. Few theorists, if any, think it is the least bit contradictory to suppose that
M is in P at one moment and then in Qa moment later.

Consider a car travelling north across Texas during a three-hour temporal
interval. Let us suppose it is in the centre of
Lubbock
at 08:00am and in the centre of
Amarillo
(approximately 124 miles away) at 11:00am. In that case, it will have been in
two locations during the same temporal interval(lasting three hours), but not in two places in
the same moment in time. In this case, the alleged contradiction has disappeared.
Indeed, this car won't even be in Lubbock and not in it at, say, 08:01,
even while it is moving -- since it will be in Lubbock for several minutes
(until it reaches the city boundary). So, in this instance, the car isn't in one place
and not in it in this sub-section of the interval. If that is so, only a very
short-sighted DM-fan will want to take advantage of this escape route (no pun
intended) -- i.e., referring to temporal intervals as opposed to 'moments in
time'. This is probably why Engels didn't refer to temporal intervals, and,
as far as can be ascertained, no DM-theorist has done so since.

On a different tack: Do these contradictions
increase in number, or stay the same, if an object speeds up? [This is a problem
that, for example, exercised Leibniz; more on this
below.] Or, are the two
locations
depicted by Engels (i.e., the "here" and the "not here") just further apart? That is, are the two points that M occupies at the same
moment, if it accelerates, just further apart? But, if it occupies them at the
same time, it can't have accelerated. That is because it hasn't moved from
the first to the second, since it is in both at once. Speeding up,
of course, involves covering the same distance in less time, but that isn't
allowed here, nor is it even possible. In which case, it
is far from easy to see how, in a DM-universe, moving bodies can't possibly
accelerate if they are in these two locations at once.

[I am of course using "accelerate" here as it is
employed in everyday speech, not as it is used in Physics or Applied
Mathematics.]

Accelerated motion (in the above sense of this
word) involves a body being in (or
passing through) more places in a given time interval than had been the case
before it accelerated. But, if M is in these two places at the same time,
how can it pick up speed?

Quite apart from this, Engels's endeavour to provide an overtly linguistic,
or even 'conceptual', solution to the
'problem of motion' suggests that
there is more than a hint of
LIE to his theory. And no wonder:
he lifted this approach from Hegel, an
Idealist of the worst possible kind.

This
'conceptual' approach
to motion is evident from the way that Engels's depiction of it depends on a
'one-sided' consideration of just a handful of the
concepts that seem to be relevant
in this area -- expressed, though, by means of some rather ordinary-looking words, the
meaning of which Engels simply took for granted (more on this later).

So, based on thought alone, Engels imagined he could conclude what must be true
of every moving body in the entire universe, for all of time,
without exception. But, how could he possibly have known all this with
so little evidence (in fact, no evidence at all, as we will also see) to back it
up?

"[S]o long as we consider things as at rest and
lifeless, each one by itself, alongside and after each other, we do not run up
against any contradictions in them. We find certain qualities which are partly
common to, partly different from, and even contradictory to each other, but
which in the last-mentioned case are distributed among different objects and
therefore contain no contradiction within. Inside the limits of this sphere of
observation we can get along on the basis of the usual, metaphysical mode of
thought. But the position is quite different as soon as we consider things
in
their motion, their change, their life, their reciprocal influence on one
another. Then we immediately become involved in contradictions. Motion itself is
a contradiction: even simple mechanical change of position can only come about
through a body being at one and the same moment of time both in one place and in
another place, being in one and the same place and also not in it. And the
continuous origination and simultaneous solution of this contradiction is
precisely what motion is." [Engels (1976), p.152.
Bold emphasis added.]

"Motion is the mode of existence of matter.
Never anywhere has there been matter without motion, nor can there be….
Matter without motion is just as inconceivable as motion without matter.
Motion is therefore as uncreatable and indestructible as matter itself; as
the older philosophy (Descartes) expressed it, the quantity of motion existing
in the world is always the same. Motion therefore cannot be
created; it can only be transmitted….

"A motionless state of matter therefore proves to
be one of the most empty and nonsensical of ideas…." [Ibid.,p.74. Bold
emphases alone added.]

Notice, Engels explicitly contrasts what we can see (when he refers to the
"limits of this sphere of
observation")
with how things seem when we "consider things". In other words, his only
'evidence' is based on how we think about motion not what we see in
relation to it.

Clearly, Engels was
in possession
of a truly remarkable skill:
the ability to uncover fundamental features of reality, valid for all of space and time,
from the alleged meanings
of a few words, or 'concepts'! Indeed, Engels's claims about motion are all the more
impressive when it is recalled that he hit upon them in abeyance of any
supporting evidence
-- let alone a significant body of it. As it
turns out (and this will also be demonstrated below), even had any evidence been
available to him, it would have been
unnecessary, anyway.

As we have already seen (in Essay
Two), all that an aspiring dialectician
like Engels needs to do in such circumstances is briefly 'reflect' on the supposed meaning of a few words,
or 'concepts',
and substantive truths about fundamental aspects of nature, valid for all
of space and time, spring instantly to mind.

Or, to be more honest, all
they have
to do is read Hegel's 'Logic' (or the work of some other mystic, such as
Heraclitus).
This
a priori approach to 'knowledge' is the thread that runs through the
entire history of ruling-class thought,
unfortunately imported into the workers'
movement by incautious non-workers like Engels. [On this, see Essay Nine
Parts One and
Two, Twelve
Part One and Fourteen Part Two.]

The
only 'evidence' that 'supports' Engels's interpretation of motion is
this highly compressed (and, as we will see, rather
badly formulated) argument -- or rather, 'thought experiment' --, which is itself based on a consideration of what
a few innocent-looking words, or 'concepts', must mean. Pressed for a justification of
his line of reasoning, all that Engels could possibly have offered would
have been a rather weak claim
that this is what the word "motion" really means. Clearly, such
a rejoinder would give the game away, since it would reveal that
substantive truths about motion had indeed been derived from the supposed meaning of
a few words, and
nothing more.

[The significance of that observation will emerge in Essay Twelve
Part One.]

As noted above, an appeal to
evidence would be irrelevant,
anyway. That is because the examination of countless moving objects would fail
to confirm Engels's assertion that they occupy two places at once. That would
still bethe caseno matter what instruments or devices
were employed
to effect these hypothetical observations, and regardless of the extent
of the magnification used to that end -- or, indeed, the level of microscopic detail enlisted in
support. No observation could confirm that a moving object is in two places at
once (except in the senses noted below), in one of these and not in it at the
same time. That explains, of course, why
Engels offered no scientific evidencewhatsoever in support of his belief
in the contradictory nature of motion. And the picture
hasn't altered in the intervening years -- indeed, the author of no book, article,
or talk about DM even so
much as thinks to quote or cite such evidence --, and this situation isn't ever likely to change.5

It could be
objected to this
that if,
say, a
photograph were taken of a moving object, it would show by means of the recorded
blur, perhaps, that such a body had occupied several places at once. In
that case, therefore, there is, or could be, evidence in support of Engels's
claims.

The problem with this is that no matter how fast the shutter speed, no
camera (not even
this
one, or
this) can record an
instant in time, merely a temporal interval -- that is, such devices
record what happens in the time
interval between opening and closing the shutter, or other light permitting
aperture. Clearly, to verify the claim
that a moving object occupies at least two places in the same instant, a
physical recording of an instant would be required. Plainly, since
instants (i.e., in the sense required) are mathematical fictions, it isn't
possible to record them.

Update December 2016: The New Scientist recently reported
this:

"For the first time, physicists have measured changes
in an atom to the level of
zeptoseconds, or trillionths of a billionth of a second -- the smallest
division of time yet observed. In this case, the speed demon was an electron
escaping the bonds of its parent atom when struck by a photon. This electron
ejection is known as the photoelectric effect, and was described by Albert
Einstein in 1905. Previous experiments could only measure what happened after
the electron was kicked out, says Martin Schultze at the Max Planck Institute of
Quantum Optics in Garching, Germany. Now, he and his colleagues have measured
the ejection of electrons from a helium atom from start to finish with
zeptosecond precision (10-21 seconds), marking
the smallest time slot ever measured. To do this, they fired ultraviolet laser
pulses lasting 100 to 200 attoseconds (10-18
seconds) at a helium atom to start exciting its pair of electrons. By making
many readings and calculating their statistical spread the team could measure
events with a resolution of 850 zeptoseconds. They found the ejections took 7 to
20 attoseconds (Nature Physics,
doi.org/bszd). The results are an important window into the quantum
behaviour of atoms, especially how their electrons interact with each other,
says Schultze." [New
Scientist, 19/11/2016, p.14. Paragraphs merged to save space.]

Not
even this measurement captures an 'instant', just an interval.

It could be countered that as
we increase a camera's shutter speed, photographs taken will always show
some blurring. This
supports the conclusion that moving objects are never located in one
place at one time. Despite this, it still remains the case that no photograph
can catch an instant, and thus none can verify Engels's contention.

Again, it could be argued that it is
reasonable to conclude that moving objects occupy two locations at the same
moment from the above. Once more, since an instant in time is a fiction, it
isn't reasonable to conclude this.
Not even a mathematical limiting process could capture such ghostly 'entities'
in the physical world, whatever else it might appear to achieve in theory. But, even
if itcould,
no camera (radar device, or other equipment) could record it. Hence, even
if an appeal to a mathematical limiting process was viable (or available), it
would be of no assistance. No experiment is capable of
substantiating any of the conclusions Engels reached about moving bodies.

And
that explains why he and those who accept these ideas have had to
foist this view of motion onto nature.

But, as we will see later, the idea that a moving
object is in two places at once possesses rather nasty consequences of its own for this
theory, so DM-fans had better hope that no camera will ever be able to record
this alleged fact.

Hence, Engels's thesis about moving bodies
wasn't derived from
a consideration of the facts, it has been imposed on them, in defiance of what Engels himself said:

"Finally, for me there could be no question of
superimposing the laws of dialectics on nature but of discovering them in it and
developing them from it." [Engels (1976),
p.13. Bold emphasis
added.]

"All
three are developed by Hegel in his idealist fashion as mere laws of thought:
the first, in the first part of his Logic, in the Doctrine of Being;
the second fills the whole of the second and by far the most important part of
his Logic, the Doctrine of Essence; finally the third figures
as the fundamental law for the construction of the whole system. The mistake
lies in the fact that these laws are foisted on nature and history as laws of
thought, and not deduced from them. This is the source of the whole forced and
often outrageous treatment; the universe, willy-nilly, is made out to be
arranged in accordance with a system of thought which itself is only the
product of a definite stage of evolution of human thought." [Engels
(1954),
p.62. Bold emphasis alone added.]

"We all agree that in every field of science, in natural
and historical science, one must proceed from the given facts, in
natural science therefore from the various material forms of motion of matter;
that therefore in theoretical natural science too the interconnections are
not to be built into the facts but to be discovered in them, and when discovered
to be verified as far as possible by experiment.

"Just as little can it be a question of maintaining the
dogmatic content of the Hegelian system as it was preached by the Berlin
Hegelians of the older and younger line." [Ibid.,
p.47. Bold emphasis alone
added.]

In which case, the following characterisation of Idealism clearly applies to
Engels's 'analysis' of motion:

"A consistent materialism can't proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphasis added.]

But, this is precisely what Zeno and Hegel did,
just as it accurately describes Engels's approach; they all "proceed[ed] from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source."

Of course,
as noted above, part of the problem here is what the word "instant" means.
[I am taking this term to mean the same as the phrase "moment in time", used by Engels.] So, it might be
thought that it might be possible to solve this 'problem' by means of a suitable re-definition.
However, even if that were possible, such an 'adjustment' would merely represent
the adoption of a new linguistic convention, and would have no bearing at all on the
'nature
of reality'. It would also further confirm the suspicion that this 'theory' had
been imposed on nature, not 'read from it' -- for what else is the introduction of
a new linguistic convention, adopted solely in order to make a theory 'fit the
facts', but an imposition?5a

"How should we really conceive the word 'moment'? If it is an
infinitesimal interval of time, then a pound of sugar is subjected during the
course of that 'moment' to inevitable changes. Or is the 'moment' a purely
mathematical abstraction, that is, a zero of time? But everything exists in
time; and existence itself is an uninterrupted process of transformation; time
is consequently a fundamental element of existence. Thus the axiom 'A' is equal
to 'A' signifies that a thing is equal to itself if it does not change, that is
if it does not exist." [Trotsky (1971), p.64.
Bold emphasis added.]

Unfortunately for Engels, if motion were
to take place in one of these "moments", that would mean it couldn't
exist -– that is, not unless we are also prepared to reject the a priori
opinion Trotsky expressed in the above passage, too!

But, if motion actually takes place -- as it surely does -- then what are we to make of
the claim that if something is moving it must be in at least two places in the
same instant when (according to Trotsky) the latter don't exist? Does
this refute Trotsky? Or Engels? Or both? Is there even a straw-sized
'contradiction' here for dialecticians to "grasp"
to save their drowning theory?

Furthermore, pointing out that some of the conclusions drawn above are rather
abstract can't rescue Engels, either. His
analysis of motion is no less abstract itself! Even worse: his account can't have been
derived by abstraction from all (or any) of the forms of motion hitherto
experienced either by himself or by humanity in general -- or even from a finite
sub-set of them, observed by scientists or philosophers down the ages. That is because
Engels's thesis clearly appeals to things that, according to Trotsky, don't exist --
such as "moments" in time. And, even if they
did exist,
we couldn't experience or observe them, and hence we couldn't use them to
confirm what Engels said. As seems plain, observations take place in time, and have a duration;
"instants" do not.

Even worse still, it isn't possible to 'abstract' from such
non-existent instants in order to
agree with Engels, either.6

To be
sure, Engels promptly changed direction (no pun intended, again) in the above passage, arguing that it is
motion itself that is contradictory, not just our thoughts about it that
are -- declaring that:

In which case, it could be maintained
that Engels was merely pointing out that our thoughts about motion are
contradictory because motion itself is. That is, our theories
depict the world more fully and truly when they reflect its contradictory nature, and,
further,
that substantive claims about the universe are justified, indeed, objective, when our ideas capture
changing reality more accurately (but, only if they have been tested in practice).

Unfortunately, if this response were correct, it would be inimical to DM,
anyway,
since that would mean DM
itself contains contradictions, which would imply it is a contradictory
theory!7

[The disastrous implications that particular conclusion has for DM are outlined in Essays
Seven Part One and
Eleven Part One.]

Despite this, such a reply would give the game away, since it conforms
an earlier accusation that this view has been imposed on nature because there is
no way that Engels could know, or have known, that nature is contradictory in its entirety, and thus
that all motion in the entire universe, for all of time, is as he says it is. The very best that
Engels could claim is that our thoughts about motion are contradictory, and that this
suggests that motion in nature might be, too.

However, as will become apparent by the end of this Essay, the real problem with the
above suggested fall-back position is that
our thoughts about motion
aren't the least bit contradictory, either!7a

Be this as it may, the above response fails
anyway to neutralise the fatal
consequences
outlined
earlier.
That is because Engels's philosophical thesis,
which was the result of an extrapolation from what he took to be the meaning of a handful of words
or 'concepts' to fundamental aspects of reality,
is openly Idealist (on this see Essays
Two and Twelve
Part One).
Indeed, Engels himself pointed this out:

"The general results of the investigation of the world are
obtained at the end of this investigation, hence are not principles, points
of departure, but results, conclusions. To construct the latter in
one's head, take them as the basis from which to start, and then reconstruct the
world from them in one's head is ideology, an ideology which tainted every
species of materialism hitherto existing.... As Dühring proceeds from
"principles" instead of facts he is an ideologist, and can screen his being one
only by formulating his propositions in such general and vacuous terms that they
appear axiomatic, flat. Moreover, nothing can be concluded from them; one
can only read something into them...." [Marx and Engels (1987), Volume
25, p.597. Italic emphases in the original; bold emphases added.]

"A consistent materialism cannot proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphasis added.]

Worse still, and
for reasons given above, not only can this
'theory' not be confirmed, its subject matter (i.e., the thesis that a
moving body occupies and does not occupy the same place in the same moment,
being in two places at once) resists all attempts to make sense of it, as we
will soon see.

Substantive
philosophical 'truths' like this (about motion, for example) are ambitiously universal in
intent, but are thoroughly parochial in origin. Indeed,
their promulgators' epistemologically imperialist intentions (which purport to stretch
across all regions of space and time) remain stubbornly unmatched
by any obvious capacity to satisfy such excessive philosophical ambitions with adequate
material evidence --, or, in this case, any at all.

More to the point,
how can
this thesis be 'tested in practice'?

As we have seen,throughout history Traditional Theorists
-- like Engels, and
more particularly, Hegel -- have privileged speculation ahead even of a
perfunctory search for supporting evidence. Indeed, they assumed that all of nature
must be as their 'specially-concocted' terminologyappeared to depict it.

However, if this
approach to Super-Truth
were valid, it would mean that the universe
was possessed
of these features simply because of the idiosyncrasies
of Indo-European Grammar -- the language group in which most of this hyper-bold talk
had been concocted.

Perhaps even worse still:
It isn't
easy to see how the 'contradictory' nature of motion could in any way explain it;
nor
is it easy to see how it could form part of a wider scientific account of anything
at all. At best,
this way of characterising motion simply re-describes it.

More
specifically: it is difficult to see how one 'part' of this supposed 'contradiction' is
capable of exercising a causal
influence over any other 'part'; or,
indeed, how one or both of these UOs (presumably, this "here" and this "not
here")
could actually make anything move.

[A more
general objection to this way of seeing change has been posted
here. I am assuming there is a UO
here, which there would have to be if this were a 'dialectical contradiction',
and the only viable candidate seems to be "here" and "not here". Exactly how
these two are supposed to 'struggle' with one another --
which the DM-classics tell us is an "absolute" -- is therefore something of
a mystery. More on this
below.]

[UO =
Unity of Opposites.]

As
Engels depicts things, both 'parts' of this UO appear to manifest themselves together; a
body is "here" and "not here" all at once, as it were:

"Motion itself is a contradiction; even simple mechanical
change of place can only come about through a body being both in one place and
in another place at one and the same moment of time, being in one and the same
place and also not in it." [Engels (1976),
p.152.]

In that
case, it looks like
awkward questions concerning the proximate cause of motion (with the implied
temporal concomitants these often motivate) can't be
answered by anyone who accepts this way of depicting it. That is because the mere fact
that a moving body is "here" doesn't appear to be capable of making it become "not here".
There is no struggle going on between this "here" and this "not here",
again, as we were told by the DM-classicists should be the case with all such
'dialectical contradictions'. Indeed, this alleged contradiction
seems to lack anycausal power, any capacity to make
something happen. It isn't so much that the dialectical batteries have run down as
it is that there don't appear to have been any supplied
with the original article -- nor is there anywhere for them even to slot into.

This probably explains whyEngels didn't even
attempt to construct a causal account of motion based on the contradiction
he claims to have found here (and, as far as can be ascertained, no DM-theorist
since has made any effort to fill in the gaps -- and that includes Graham Priest). But, even if a DM-causal account were
to be provided (one day!), it isn't easy to see how these alleged contradictions could explain motion
--
after all, how does
being "here" and "not here" (all at once) explain why
anything
actually moves? What work do such contradictions do -- even if you believe in them?

It could be objected that this radically misconstrues DM, for the
counter-argument presented above misleadingly splits
the assumed 'parts' of a contradiction from one another when DM itself requires
contradictions to be constituted by (or to be based upon) interpenetrated
opposites. A dialectical contradiction is a relation, not a thing.
Moreover, and contrary to the above, DM doesn't depict motion or change in such
mechanical, causal terms. Dialecticians' various discussions of
causation
are specifically aimed at countering mechanistic and reductionist
accounts like this.

Or, so a response might go.

However, even if this reply
were acceptable, no attempt was made in Engels's work -- and, to my knowledge, none has
been made anywhere else -- to explain how contradictions can have
any effect on anything at all, anywhere, anyhow, and in whatever
preferred causal or mediational/dialectical language they are expressed -- that
is, other
than perhaps figuratively. [There is more on this in Essay Eight Parts
One and
Two.] And, this is quite apart
from the fact that this alleged contradiction (in motion) doesn't appear to be relational
at all. What precisely is being related to what? What "relation" is this
particular example meant to picture or reflect? Is a body related
to itself as it moves? But, even if it were, how would that make it move?

[One
of the best 'dialectical' attempts that I have so far seen (and written by a Marxist
Dialectician, too) to explain the
rationale behind this view of motion and change has been taken apart
here. In Note 18a, I am in process of doing
something similar (but on a smaller scale) to another attempt to account for
motion -- this time found in
Graham Priest's work, but which might not actually be a 'dialectical-explanation',
after all.]

Of course, it could be argued that it is the relation between
bodies and processes that makes objects move and change; that response will be examined below, and in more
detail in Essay Eight Part Two,
as will the idea that contradictions can be accounted for in terms of "opposing
forces".

Moreover, it is far from easy to see how a contradiction could exercise any sort
of effect on anything at all unless it was translated into, or was expressed somehow
in,
physical or material terms. [That will be attempted below.] At some point,
parcels of
matter are going to have to be moved about the place. Now, this
physically inconsequential word ("contradiction") doesn't seem to have the
required presence -- the necessary oomph, as it were --
that might conceivably enable it to carry out such menial tasks.8

[HM = Historical
Materialism.]

Furthermore, if the volunteered
DM-response above were correct
(but see below),
contradictions wouldn't be of much
help in explaining social change, let alone any changes in nature. If no
causal role is assignable to contradictions in DM (with respect to motion,
or, indeed, with respect to anything at all), then they certainly can't serve in
such a capacity in HM, can they? The alleged contradictions in Capitalism, for example,
wouldn't, therefore, make anything actually happen if the latter were the case; they would, at best, be the
result of other things happening (incidentally, for which DM-theorists would now have no
explanation, since these 'other things' wouldn't themselves have been caused by
contradictions), or they would be the result of
certain specific social relations.

The cause or causes of social development would be totally
obscure (given this (assumed) rejection of any causal role for contradictions in
DM). In that case, we are forced to conclude
that if there are contradictions in reality, they must
play some sort of causal role, at some level, in some form,
otherwise dialecticians wouldn't be able to explain why anything actually happened
in nature and society.

[Of course, that might be the real reason why
dialecticians can't
actually do this; but they certainly don't see things this way -- to
state the obvious.]

Conversely, this could mean that if the development of class society is still to
be accounted for in terms of the supposed contradiction between the forces and
relations of production -- or even between opposing classes -- contradictions could be dispensed with at no loss to HM, since (given the above
response) contradictions would do no work in HM, too -- playing no causal
role there. In that case, the sooner they are pensioned-off the better. Attention
could then be focussed on the genuinely causal nature of the above relations --
suitably phrased in historical and materialist terms. Naturally, this would involve a radical
re-write of HM, abandoning much of the traditional,
Hermetically-inspired jargon,
which has up until now only succeeded in suffocating Marxist theory.

If
so, this means that
dialecticians need to specify -- as a matter of some urgency, I would suggest -- what, if
anything, is so causal about the contradictions they seem to see
everywhere, so that the latter can at least do some genuine work in HM. At
present they don't appear to
be part of the action; at best, they look merely decorative.

On the other hand, the assignment of a causal role to contradictions in HM or DM
-- so that they cease to be merely ornamental -- would generate insuperable difficulties for
both theories, as we are about to see.

As hinted above, even if it were possible to assign some sort of causal role
to contradictions (albeit expressed in suitably acceptable 'dialectical
language'), it would still fail to help DM-theorists account for motion. That is
because (according to Engels) motion allegedly involves a body being in one
place and not in it, all the while being in two places at one and the same
'instant', or 'moment'. The problem is: How does this actually explain
motion causally -- or, indeed, in any other sense? What exactly does it add to a
scientific account of the same phenomenon? All it appears to offer is a
paradoxically-worded re-description.

In order to make the last point a little clearer, it
might be worth pondering once again the
possible DM-answer(s) to the following questions:
(a) Do
contradictions cause motion (i.e., do they make objects move), or (b) Does motion merely
reveal the presence of contradictions as it unfolds?

"[S]o long as we consider things as at rest and
lifeless, each one by itself, alongside and after each other, we do not run up
against any contradictions in them. We find certain qualities which are partly
common to, partly different from, and even contradictory to each other, but
which in the last-mentioned case are distributed among different objects and
therefore contain no contradiction within. Inside the limits of this sphere of
observation we can get along on the basis of the usual, metaphysical mode of
thought. But the position is quite different as soon as we consider things in
their motion, their change, their life, their reciprocal influence on one
another. Then we immediately become involved in contradictions. Motion itself is
a contradiction: even simple mechanical change of position can only come about
through a body being at one and the same moment of time both in one place and in
another place, being in one and the same place and also not in it. And the
continuous origination and simultaneous solution of this contradiction is
precisely what motion is." [Engels (1976), p.152.
Bold emphasis added.]

On one
reading of Engels's account, it looks like it is motion that causes (or
creates) these contradictions. Hence, according to this way of reading his exact words, something must be in
motion first for it to bring about contradictory, simultaneous occupancy
and non-occupancy of successive locations (while time advances no one
nanosecond). But, as we will soon see, this would
mean that one or both of the following hypotheticals would have to be true:

(1)If
there were no contradictions, movement could still take place.

(2)If movement ceased, contradictions would still
remain.

Taking each in turn:

(a)
The relevance of the first alternative is
underlined by the fact that unless motion was already present, no
contradiction could
be inferred.

At the very least, this option prompts a
further question: Which came first, the movement or
the contradiction? One possible answer to this might be what lay behind Engels's
comments that these contradictions could be "solved", then "re-asserted", since, on that basis, it looks like motion
causes
contradictions, not the other way round.

Of course, it could be argued that these two
factors (i.e., contradiction and motion) go hand-in-hand; so
it no more makes sense to ask which came first, movement or contradictions than
it would to ask: "Which came first, counting or numbers?"

But, as we will see later on in this Essay, there are (in fact) examples of
motion (in the real world) where no 'contradiction' is implied, directly or
indirectly. So, perhaps that is the case here, too?8a

(b) The second option above follows from the simple observation that a stationary
body can also occupy two places at once, and it can be in one place and not in
it at the same time. [Examples of both of these alternatives are given
below.]

In that case, alternative (2) suggests that contradictions aren't a
sufficient
cause of motion, whereas (1) indicates they aren't evennecessary.

(1)If
there were no contradictions, movement could still take place.

(2)If movement ceased, contradictions would still
remain.

Furthermore, and with respect to (1), once again: Engels himself appears to
have
reasoned from his understanding of what motion is to its alleged contradictory
implications. In that case, it looks as if there is no causal role
for contradictions to play with respect to 'motion itself', at least, as far as Engels saw things -- that is, there seems to
be no way that contradictions could make anything move. At best, a noted above, they appear to be
conceptually derivative, not causative; they depend on motion, not the other
way round. Hence, as things now stand,
it looks like bodies first of all move, and only then
do contradictions emerge -- and even then this only applies to our depiction of motion.

If so, it might be correct to say that contradictions operate solely at the conceptual
level -- they appear to have no part to play in the physical action, on
the ground, as it were.

Given
this 'modified view', it would seem that objects in the world just move, but
they don't to do so because they become embroiled in
literal contradictions.

[So,
for example, moving bodies don't argue among themselves about the
occupancy or non-occupancy of this or that particular "place" --, which would be the clear
implication of the ordinary, literal use of the verb "to contradict". Nor do
they become entangled in 'time-and-motion' wrangles about who or what was where,
when, or why. Again, they would do this if
literal contradictions (as opposed to a figurative, DM-extension to
this word) were operative in such cases. (On this, see Note 1, and Essay Eight Parts
One and
Three.)]

In fact, given Engels's account of
motion, it seems that it is we who derive these paradoxical conclusions in
our attempt to depict something that just takes place (without any such fuss) in nature.

In other words,
according to this interpretation of Engels's views, it looks like the 'fault'
lies in us, not in
objects and processes.

However, this
way of depicting motion is clearly unacceptable to DM-theorists; they insist
that we must begin with material reality (or our perception of it), and not
simply with a description.
From there, according to them, we must postulate only those contradictions that
actually exist in nature and society -- based perhaps on their reflection in human
thought, confirmed in practice. Clearly, human beings study
motion and its attendant contradictions, using whatever conceptual resources they have
to hand, which, unfortunately, might not always be up to the job.

Or, so a counter-claim might
go.

But, even
this response is no help. That is because there seems to be
nothing in reality that thought could latch onto, or reflect -- and hence, nothing for
anyone to abstract from, or to, and then test in
practice -- that even remotely resembles the contradictions postulated by
dialecticians.

[Why
that is so occupies the last three quarters of this
Essay -- as well as
this one.]

In relation to Engels's account of motion, as will soon
become apparent, there is no clearly
specifiable set of possibilities -- or even actualities -- in nature or society with which his description
could conceivably correspond. In
fact, his words turn out not to be a depiction of the physical world in any
shape or form. That isn't because he got the details wrong, or because he failed to capture nature
accurately enough --, nor yet because nature is too complicated for us to
describe -- it is because his words fail to be adescription to
begin with.
Hence, Engels's 'description' of motion isn't just empty, it isn't even a
description!

It turns out to be far too vague and
incoherent to count as one.

Again, it could be objected that the analysis presented in this Essay is misguided since it
compartmentalises reality, distorting the account of nature presented in DM.

In response, it is worth pointing out that we don't have to divide
the 'parts' of a contradiction, one from another (or from other relevant aspects
of reality), to make the above argument work.

If each and every contradiction postulated by dialecticians (whether derived
from "really existing material forces", or not) is given a sufficiently complex,
'dialectical background' (interconnected within the Totality, required by the
theory, verified in practice, etc., etc.), that still wouldn't amount to an explanation
of the causal, or "mediated", links that are required by this theory. Widening the
domain (to the entire Totality if need be) can't suddenly provide an explanation of how
the simultaneous presence and absence of an object in one and the same place
at the same time
could possibly make it move -- or even how it could account for motion in
any way at all.

An appeal to forces here would be to no avail, either -- as will be
demonstrated in detail in Essay Eight
Part Two. Unless forces are anthropomorphised, they, too, can't account for
movement and change in DM-terms, either. [That cryptic comment will also be explained in
Essay Eight Parts One and
Two.]

Furthermore, the alleged reflection
of contradictions 'in the mind', which might be thought capable of providing the 'conceptual
connection' that supposedly exists between a cause and its effects (or between various mediated items, objects,
or processes in the Totality), can't create a genuine
connection if there aren't any contradictions in reality for it to reflect.
Contradictions must have some sort of material basis if they are to be
reflected in thought; for materialists they can't just be conceptual. And yet, what material
form do these contradictions take?

Unless some sort of sense can be given to the idea that contradictions are capable of connecting
things in the required way -- inreality and not just 'in the
mind' --, in order to provide grist for the DM-causal/mediational
mill to grind away at, DM-style reflections would advance the explanation of motion
not one nanometre.

Even assuming it could be shown that contradictions do in
fact
represent a material, or physical, relation between objects or processes -- and which have been abstracted from
(or read into) the phenomena
(in an as yetunspecified way!) -- they
still couldn't account for motion. That is because this would simply amount to a
re-description of the phenomena, once more. We still await the explanatory punch-line: how do
contradictions make things move? What is the materialpoint to this Hegelian
myth? Where does the rubber hit the road (to use an Americanism)?

If, though, it is now claimed that a causal (mediational) link of this sort between events must to
be postulated (i.e., if it is just assumed to exist to make the theory work), then that would merely provide a conceptual
link between the said events, once more -- and such it would remain until the
physical details had been filled in. Without the latter the contradictory nature
of motion would remain at best a conceptual, but not yet a material aspect of reality.

If, on the other hand, it is claimed that the mere presence of the said conceptual
connection indicates that these causal links must exist in reality -- that is, if
the complex reflection theory of knowledge is assumed to be true (wherein the
human mind actively acquires knowledge in practice, etc.) --,
then that would still fail to explain how contradictions could actually cause
motion. Precisely how do contradictions succeed in moving things about the place?
It would seem that here the dialectical spade isn't just turned, it snaps in two.

Clearly, the above difficulties will only be resolved at some point if a clear
explanation is given as to how contradictions can make anything move -– or, at least,
until it is shown how and in what way the above objections are misguided.

However, as should now seem plain, the role that contradictions supposedly play
in motion is hardly helped by an account that depicts them: (a) As a product,
not the cause, of motion (implying they are derivative, at best), or
(b) As a consequence of human reflection (on the nature of motion, which would
suggest
they are merely conceptual, and hence Ideal).

Hitherto,
DM-theorists have been content
merely to label certain states-of-affairs
"contradictory" without (apparently) giving any thought to the lack of explanatory
role this empty ceremony assumes in their theory. Why call anything "contradictory" (and claim
so much for the use of this term) if no account can be given of how this explains
how or why anything
actually changes or moves?

At this point, it could be argued that the above objections are all irrelevant since
DM-theorists are committed to the thesis that motion and change are caused by
internal contradictions; the above account seems to be obsessed with
external causes.9

Unfortunately, in connection with motion, there don't appear to be any internal
contradictions capable of impelling objects along. No one supposes
(it is to be hoped!) that an internal contradiction works like some sort
of metaphysical motor, humming away inside a moving object, powering it on its
way!9a
Moreover, there don't seem to be any 'struggles' taking place within moving bodies
that impel them onward (perhaps in the way that a drunken brawl might make a train carriage
wobble from side to side, only worse). And, this would still be the case evenif it were true that all bodies
were in fact UOs. No matter how intense this
supposed internal battle becomes, a
'metaphysical boxing match' of this sort seems incapable of generating self-propulsion.

Lenin's "demand", therefore, looks rather empty (if
this is what he meant):

"Dialectics requires an all-round
consideration of relationships in their concrete development…. Dialectical logic
demands that we go further…. [It] requires that an object should
be taken in development, in 'self-movement' (as Hegel sometimes puts it)…." [Lenin
(1921), p.93. Bold emphases added. This entire topic is examined in
much greater detail in Essay Eight Parts
Oneand Two.]

Furthermore, there don't appear to be any identifiable contradictions situated
at the leading edge of a moving body 'dragging' it along, as it were, just as there seem to
be none at the
back 'pushing'.

Worse still: both of these scenarios (even if they were remotely
plausible) would clearly involve the creation of kinetic energy out of thin
air. For example, precisely which "internal contradictions" keep a billiard
ball moving?

In that case, with regard to individual bodies, motion can't be
an example of change through "internal contradiction".

However, as we will see in Essay Eight
Part One,
part of the problem here is that DM-theorists
equivocate between two meanings of
the phrase "internal contradiction". Sometimes it refers to (i) A
dialectico-logical "internal relation" between objects and processes; sometimes
it (ii) Assumes a spatial connotation. So, an "internal contradiction" of the
first sort could still exist between two spatially separated bodies (they would
be 'logically' connected, or would 'mediate' and/or define one another); whereas
examples of the second sort would seem to occur inside a given body, process or
system (which would 'contradict' one another merely by 'struggling' with each
other; there would be no logical (obvious) connection between them).In which case, it is reasonably
clear that
something could be spatially-internal to an object or system without it being
logically-internal, just as something could be spatially-external while also being
logically-internal.

The expressions "internal contradiction" and "internal
relation" (or what they supposedly represent) clearly underpin the idea that
there are, or can be, internal, 'inter-penetrated' opposites. We can perhaps
illustrate what an internal opposite is by recalling what DM-theorists say about
the relation between the two main classes under Capitalism, the Proletariat and
the Bourgeoisie. It is quite clear that for DM-theorists the Bourgeoisie and the Proletariat
presuppose, inter-define and condition one another; each
provides the condition for the
other's existence; without the one the other not only wouldn't, it couldn't exist.
They are thus internally related, not externally or accidentally connected.

This is what dialecticians mean by
"interpenetration"; they don't mean these factors spatially interpenetrate one
another, but that the one cannot exist without the other, nor vice versa;
the existence of the one logically implies the existence of the other, and
vice versa. And this is where the presumed "contradiction" arises;
Proletariat and Bourgeoisie are logically locked together, they cannot exist
independently of one another. This means that they have diametrically opposed
material interests which force them into unremitting class conflict. None of this is accidental or external;
the interplay between capitalist and worker is both reciprocal and
inter-dependent.

Plainly, an external relation doesn't possess these
logical properties. Concerning any two items (i.e., objects and/or processes),
if they are externally related, the one can exist without the other; they
don't presuppose one another, nor do they inter-define each other.

But, as noted above, something can be
(a) spatially-internal to an object or system without it being logically-internal,
just as something can be (b) spatially-external while also being logically-internal.

[Indeed, something can be spatially-internal to an
object or system and logically-internal to it, too, just as something can
be spatially-external while also being logically-external, as well.]

Here is an example that might illustrate (a), above:
an Amazonian tribe is logically-external to capitalism (since there seem
to be no internal opposites in the capitalist system that condition that tribe
and which are conditioned in return by it, or which define it and which it defines in
return). Capitalism can live without Amazonian tribes, but it can't live
without the Bourgeoisie and the Proletariat. Even so, this tribe would still be
spatially-internal to the capitalist system in that it still exists in a
Capitalist country, Brazil.

Alternatively, to illustrate (b): consider the relation between, say,
tenants and their landlords. They presuppose and inter-define one another; each is the
condition for the other's existence; so they are logically-internal to one
another. However, no landlord lives inside his or her tenants,
nor vice versa. In that case, landlords and tenants, while being
logically-internal to each other are at the same time spatially-external to one
another. [Naturally, this assumes each landlord has at least one tenant!]

Of course, one could always say that landlords and
tenants are spatially-internal to whatever social or economic system they happen
to exist within, and that is the problem. As we will see (in Essay Eight
Part One), this ambiguity lies
behind the equivocation mentioned above: When we consider wider economic,
social, or even physical systems, it turns out that there are in the end no such things as
spatially-external opposites, and hence spatially-external contradictions!
Indeed, it is even arguable that there are no logically-external opposites
either!

Be this as it may, it could be replied that since locomotion and development in a system
are the result of forces
acting on bodies/processes, the contradictory nature of motion can easily be accounted for on
the basis of a network of internal, systematically-opposed forces.
This might therefore be an example of a type-(ii)
"internal contradiction". That would make the unit within which contradictions (and thus motion) occur the whole,
not the part, which seems to be the assumption underlying the comments made in
earlier paragraphs.

Naturally,
that response would make a mockery of the
claim that all objects change through self-development, or that they barrel
along because they are self-motivated. Just as it would make a mockery of
Lenin's contrast between a mechanical, 'external' account of movement and
change, and a dialectical version of the same. Given this modified 'theory', no object
would be self-motivated -- never mind what Lenin demanded -- it
would be moved by forces internal to the system of which it is a part,
but external to any object caught up in that system.

"Dialectics requires an all-round
consideration of relationships in their concrete development…. Dialectical logic
demands that we go further…. [It] requires that an object should
be taken in development, in 'self-movement' (as Hegel sometimes puts
it)…." [Lenin
(1921), p.93. Bold emphases added.]

"The
identity of opposites...is the recognition...of the contradictory, mutually
exclusive, opposite tendencies in all phenomena and processes of nature
(including mind and society). The condition for the knowledge of all processes
of the world in their 'self-movement,' in their spontaneous
development, in their real life, is the knowledge of them as a unity of
opposites. Development is the 'struggle' of opposites. The two basic (or two
possible? Or two historically observable?) conceptions of development
(evolution) are: development as decrease and increase, as repetition, and
development as a unity of opposites (the division of a unity into mutually
exclusive opposites and their reciprocal relation).

"In the
first conception of motion, self-movement, its driving force, its source, its
motive, remains in the shade (or this source is made external -- God,
subject, etc.). In the second conception the chief attention is directed
precisely to knowledge of the source of 'self'- movement.

"The
first conception is lifeless, pale and dry. The second is living. The second
alone furnishes the key to the 'self-movement' of everything existing; it
alone furnishes the key to 'leaps,' to the 'break in continuity,' to the
'transformation into the opposite,' to the destruction of the old and the
emergence of the new.

"The
unity (coincidence, identity, equal action) of opposites is conditional,
temporary, transitory, relative. The struggle of mutually exclusive opposites is
absolute, just as development and motion are absolute...." [Lenin (1961), pp.357-58. Italic emphases in the original;
bold emphases added. Quotation marks altered to conform with the conventions
adopted at this site.]

Despite this, even if systematically-opposed
forces could somehow be interpreted as contradictions -- or if they could
at least be regarded as
constituting them -- that would still fail to show how internal contradictions
could explain motion (or, rather, how they could account for a change in
motion), let alone how they could initiate it. Nor would it explain the
contradictory nature of motion itself. At best, all this would do is
appeal to the allegedly contradictory nature of the system of forces that
supposedly produced, or changed, any motion in the system. The fact that a moving body appears to be in at least
two places at once (and hence contradictory in itself while moving) is in no way
connected to whatever allegedly initiated that motion, or with whatever
now maintains it (if anything does) -- at least not obviously so. Certainly, dialecticians have yet to
connect contradictory forces themselves with the alleged fact that moving bodies
appear to be in two places at once, in and not in at least one of them at the
same time. Nor is it easy to see how this might be done evenon their behalf
(since they appear to have given precious little thought to this problem in over
140 years).

Hence, whether or not it is true that movement is
caused, or 'mediated', by a disequilibrium within a system of incipient forces
('internal' or otherwise), that still wouldn't affect the alleged fact that once
it is moving, a body appears to do contradictory things. Even given the truth of such an
'internalist', or even 'externalist', account of contradictions and forces
(i.e., assuming both (i)
and (ii) above are correct), the fact that a body is in
two places at once is a consequence of this setup. But, the "in two
places at once" (etc.) descriptor (or its physical correlate) doesn't also
cause motion in addition to the forces at work in the system. Indeed, while
forces might cause a change in motion, the alleged contradictory nature of the movement that
results from this has no part to
play in the action.

So, even if the 'internalist', or
the 'externalist', picture were correct,
Engels's analysis of motion would still amount to nothing more than a
re-description of motion; it would remain the case that motion makes bodies do allegedly contradictory
things, not the other way round. Hence, the 'contradiction' that Engels
highlights is still derivative, not explanatory.

It is worth
re-emphasising this point: even if opposing forces could explain
contradictory motion (which thesis is demolished in Essay Eight
Part Two, anyway), the nature of the
connection between the supposedly contradictory nature of motion and the forces operating on
moving bodies has still to be established. All
that the addition of opposing forces has achieved is to account for the origin
of one
contradiction (motion) in terms of another (oppositional forces). The
contradictory nature of motion itself is still locked in the descriptive mode
-- it does no work. Whether or not forces can explain any changes in motion
isn't being questioned here -- yet. Even supposing they could,
the contradictions Engels supposedly saw in moving bodies remain descriptive.
We are still owed an explanation as to why a moving body being "here and not
here at the same time" and "in two places at once", accounts for its motion, as opposed to merely re-describing it.

Of course, even supposing this view were
correct, change in motion would be causally related to
forces, but that just divorces the latter from the contradictory behaviour of
moving bodies (a point Engels himself seems to have conceded -- on that, see
Note
10). So, even if it were the case that opposing forces caused motion
(or changed it),
this still would provide no useful role for the observation that motion is
itself contradictory. As far as DM is concerned (that is, on the basis of one
particular interpretation
that appears to be inconsistent with what Engels himself said about forces
-- again, see Note 10), what seems to be important here is the alleged fact that
opposing forces are contradictory; the other notion (about the
contradictory nature of motion) still appears to be redundant; it serves no obvious
purpose, and, once more, it plays no role in the action.10

[As will be argued at length in Essay
Eight Part Two, the appeal to oppositional forces to explain
contradictions (or contradictory totalities) is no less misguided. There, it
will be argued in detail that not only is there no conceivable interpretation of
opposing forces that could account for contradictions (in FL or DL), there is no
viable literal or figurative way of depicting contradictions as
opposing forces,
nor vice versa.]

[DL = Dialectical Logic; FL = Formal Logic.]

Of course,
even more revealing is the fact that in Classical Physics forces are supposed to
change the motion of bodies; this means that the idea that something has
to maintain movement (whether it is contradictory or not) depends on an obsolete
Aristotelian theory
of motion.If so, the fact
that contradictions can't supply a causal explanation of motion is
all to the good, for if the allegedly contradictory nature of motion causedandmaintained movement, much of post-Aristotelian (i.e., Newtonian) mechanics would
have to be binned.11

But, then again, if such 'contradictions' don't, or can't,
explain motion (i.e., they don't change or initiate it),
why make such a fuss about them?

Despite the above, it could be objected that this whole line-of-argument seriously
misunderstands the nature and role of contradictions in dialectics. As John Rees
pointed out:

"[These] are not simply intellectual tools but
real material processes…. They are not…a substitute for the difficult empirical
task of tracing the development of real contradictions, not a suprahistorical
master key whose only advantage is to turn up when no real historical knowledge
is available." [Rees (1998), pp.8-9.]

Hence, it could be argued that the problem with the above criticism
is that it substitutes an abstract analysis for one that should focus on real material forces.

This objection is considered in detail elsewhere at this site (here,
here,
here,
and here), where Rees's
and other dialecticians' epistemological
and methodological claims are examined at length alongside a consideration of
the "real material contradictions", to which most DM-theorists appeal
in order to illustrate
their theory -- in tandem with the claim that dialecticians don't regard their theory as a "master key"
that unlocks all of
reality, when they clearly do. [On that, see Essay
Two.]

The allegation will also be revived (here
and here, but, more
specifically here, here and
here) that material contradictions
can't account
for change, since they are locked in the descriptive mode (and a
radically confused descriptive mode, too).

However, one further possibility hasn't yet been examined (and this
introduces a
topic
that will dominate much of the rest of this Essay): What if it is
entirely unclear what Engels was trying to say in the passage under
consideration? Indeed, what if it could be shown that he was in fact saying
nothing
at all comprehensible?

In that case, it would be completely beside the point whether or not
there are any genuine examples of "material contradictions" in nature
(at least, not in so far as Engels conceived them). Well, no
more than there would be any point in Christians, for example, trying to
locate the actual Trinity somewhere in outer space. The problem here lies not so
much with the search itself (in that it might be too difficult, or would take too
long), but with the nature and description of something that could conceivably be looked for. If we
are given nothing comprehensible to search for, plainly, no search can begin.

[As noted in Essay Six,
you can look, say, for your keys if you don't know where they are, but not if
you do not know what they are.]

But, is there any substance to these claims?

The next few sections aim to show
that there is -- and plenty more than enough.

Before an empirical investigation into the 'real' cause
and nature of motion can
even begin we need to be clear precisely what it is we are being asked to
examine, to consider. As things turns out it isn't possible to determine what Engels was trying to
say
(when he wrote the following about motion):

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Engels (1976), p.152.]

In
order to substantiate the above allegation, several further ambiguities in
Engels's account will need to be examined first.

"[B]oth in one place and in another place at
one and the same moment of time, being in one and the same place and also not in
it." [Ibid.,
p.152.]

Here, he appears to be claiming two
separate things that don't immediately look equivalent:

L1: Motion involves a body being in one place and in
another place at the same time.

L2: Motion involves a body being in one and the
same place and not in it.

L1 asserts that a moving body must be in
two places at once, whereas L2 says that it must both be in one place
and not in it, while leaving it unresolved whether it is in a second place
at the same or some later time -- or even whether it could be in morethan two places at once. To be sure, it could be argued that it is implicit in
what Engels said that these events occur in the "same moment of time",
and, moreover, that if an object isn't in a certain location it must be in a
second place, since it has to be somewhere. However, I am
trying to cover every conceivable possibility, and it is certainly
possible that he not only didn't say any of this, he didn't even intend it. [The significance of
those comments will emerge as the Essay
unfolds.]

It is also far from easy to see how a moving body can be "in one
place and not in it", and yet still be in two places at once.
If moving object Misn't located at X -- that is, if
it is not in X
--, then it can't also be located at X (contrary to what Engels
asserts). On the other hand, if Mis located at X, then it can't also not be at X!
Otherwise, Engels's can't mean by "not" what the rest of us mean by that word.
But, what then did he mean?

At this point, we might be reminded that there is
a special sort of 'dialectical' "not" [henceforth "notD"],
which, it seems, can also mean "Maybe this isn't a 'not' after all; indeed, it
is the exact opposite of 'not'". And yet, if
the meaning of "not" is so plastic, so malleable, how can we be sure we know what "motion"
and "place" mean, let alone "dialectical". If "notD"
can mean the opposite of the everyday, ordinary "not", then perhaps "motion" can
also mean "stationary", and "dialectical" can mean "metaphysical" (in the sense
of that word
intended by Hegel and Engels).

But, when a DM-theorists tells us that "notD"
does not
mean "not", what are we to say of the "not" in the middle (the one coloured
red)? If "not" can slide about effortlessly in this manner, then perhaps this
red "not" might do likewise, and mean its opposite, too? If so, when a DM-theorist
tells us that "notD"
does not
mean "not", who can say whether or not he/she actually means the following:
"'NotD'
does not not (sic) mean 'not'" -- which pans out as "'NotD'
means 'not'"; at which point the 'dialectical "not" collapses back into an
ordinary "not". A rather fitting 'dialectical inversion' if ever there was one.

Until DM-theorists come up with
non-question-begging criteria that inform us unambiguously which words don't
'dialectically' develop into their opposites and which do, the above
'reminder' can be filed away in that rather large and ever-growing bin labelled "Dialectical Special Pleading".

[Anyone who objects to the above argument
hasn't read the DM-classics,
where we are told that everything in the universe -- and that must include
words, which, it seems, do exist in the universe -- struggles with, and
then turns into, its opposite.]

Returning to the main feature: it is
important to be clear what Engels meant here because L1 is actually
compatible with the relevant body being at rest! This can be seen if we
consider a clear example -- that is, where an extended body is motionless
relative to an
inertial frame.
Such a body could be at rest and in at least
two places at once. Indeed, unless that body were itself a mathematical
point, or is discontinuous in some way, it would occupy the entire space
between at least two distinct spatial locations (i.e., it would occupy a finite volume interval
-- or more colloquially, it would take up some space or some room). But, since all real,
materialbodies are
extended in this way, the mathematical point option doesn't seem relevant.
[Anyway, it, too, will be considered below, as will the motion of 'point masses'.]

L1: Motion involves a body being in one place and in
another place at the same time.

A commonplace example of this would be where, say, a train is at rest relative to a platform.
Here, the train would be in countless places at once, but still stationary
with respect to some inertial frame.

[There are countless examples of this
everyday phenomenon, as I am sure the reader is well aware. In this and
subsequent paragraphs I will endeavour to illustrate the alleged ambiguities in
Engels's account by an appeal to everyday situations (for obvious materialist
reasons). However, these can all be translated into a more rigorous form using
vector algebra or set theory. In the last case considered below, just such a
translation will be given to substantiate that particular claim.]

Unfortunately, even this ambiguous case
could involve a further equivocation regarding the meaning of the word "place"
-- the import of which Engels clearly took for granted. As seems plain, "place"
could either mean the general location of a body (roughly identical with that
body's own topological shape, and equal in volume to that body --, or, on some
interpretations of this word, very slightly larger than its volume so that the
body in question can fit 'inside' its containing volume interval).
Alternatively, it could involve the use of a system of precise spatial
coordinates (which would, naturally, achieve something similar), perhaps
pinpointing its centre of mass, using that to locate the body, etc.

Of course, as noted above, Engels might have been referring to the motion
of mathematical points, or point masses. But, even if he were, it
would still leave unresolved the question of the allegedly contradictory nature
of the motion of ordinary material bodies -- and, how the former relate to the
latter.

It is Engels's depiction of motion that is unclear; because of
that, I
will concentrate on ordinary material bodies. Anyway, since DM-theorists hold that their theory can account for motion in the real world, the
motion of mathematical points -- even where literal
sense can be made of such 'abstract' points or, indeed, of the idea that they canmove
-- won't in general be entered into here.

[After all, if such points don't exist in physical space, they can hardly be said to move.
And even if they could, what on earth do they move into? Other points?
How does one point move into another point? In
passing, it is worth adding that Graham Priest's otherwise sophisticated attempt
to defend Hegel and Engels (in, for example, Priest (2006)) largely depends on (i) the use of
mathematical and metaphysical idealisations like these (i.e., mathematical points,
planes,
manifolds, instants in time, etc.), and (ii) interpreting the material world
as a rather complex mathematical object of some sort -- which makes much of what
he has to say of no relevance to the defence of Hegel or Engels. Quite the
reverse, in fact; it would make movement itself either impossible, or far more paradoxical than even Hegel
himself imagined -- as we will see later, for example,
here and
here.]

Turning to
L2: this option involves further ambiguities that similarly fail to
distinguish moving from motionless bodies. Thus, a body could be located within an extended region
of space and yet not be totally inside it. In that sense, it would be both in and
not in that place at once, and it could still be motionless with respect
to some inertial frame.

Here, the
equivocation would centre on the word "in". To be sure, it could be
objected that "in" has been illegitimately replaced by "(not) totally or wholly
inside/in", in the previous paragraph. Despite this, it is worth noting
that Engels's actual words imply
this is a legitimate, possible interpretation of what he said:

L2: Motion involves a body being in one and the
same place and not in it.

If a body is "in and not in" a certain place it
can't be
totally in that place, on one interpretation of these words. So, Engels's
own words allow for his "in" to mean "not wholly in".

A
mundane example of this might be where, say, a 15 cm long pencil is sitting in a
pocket that is only 10 cm deep. In that case, it would be perfectly natural to
say that the said pencil is in, but not entirely
in, the pocket -- that is, it would be both "in and not in" the pocket at the same
time (thus fulfilling Engels's definition) --, but still at rest with respect to some inertial frame.
No one would think that NN was lying if she said she had a pencil in her
pocket if the above were the case. L2 certainly allows for such a situation, and Engels's use of the word "in" and
the rest of what he said plainly carry this interpretation.

Hence, it
seems that Engels's words are compatible with a body being motionless
relative to some inertial frame!

What
is more, this is still the case even when L1
and L2 are combined, in the way Engels intended they should:

L3: Motion involves a body being in one place and
in another place at the same time, and being in one and the same place and not
in it.

An example of
an L3-type
--
but apparently
contradictory -- 'lack of motion' would involve a situation where, say, a car is
parked half in, half out of a garage. Here the car is in one and the same place
and not in it ("in and not in" the garage), and it is in two places at once (in the garage
and in the driveway of a given house),
even while it is at rest relative to a suitable inertial frame.

In which
case, the alleged contradiction that interested Engels can't be the result ofmotion (since his own words are compatible with a body being at rest --
that is, what he alleged isn't unique to moving bodies).

At best, it is in fact a consequence of the vagueness, or the ambiguity, in his
sketchy description of moving bodies.

Objects at rest relative to some inertial
frame can and do display the same apparent 'contradictions' as
those that are in motion (with respect to the same inertial frame). Naturally, if
bodies
at rest share the very same vague or ambiguous features (when expressed in language) as those
that are in motion, then Engels's description clearly fails
to pick out what is unique to
moving bodies.

This isn't a good start.

We
still lack a clear and unambiguous DM-description of motion!

[Of course, it might prove possible to repair
Engels's attempt to depict 'dialectical motion'; I will leave that
for others to decide. However, given what we will soon discover about the
language associated with this topic (especially when that language has been
incorporated into a 'philosophical
theory' about motion), scepticism is perhaps the best policy.]

Again,
at
best, L3 depicts the necessary,
but not the sufficient conditions for motion. [But, as we will also see,
not even this is true.]

If so, the alleged contradictory nature of L3 has
nothing to do with any
movement
actually occurring since Engels's word also apply to bodies at rest,
which plainly share the same necessary conditions.

L3: Motion involves a body being in one place and
in another place at the same time, and being in one and the same place and not
in it.

As already noted, 'paradoxes'
like this arise from the ambiguities implicit in the language Engels himself
used -- and, as it turns out, in the language hemisused.

[This
will be discussed in greater
detail below.]

Nevertheless, in the next few sections several attempts will be
made to remove, or resolve, these
equivocations in order to ascertain what, if anything, Engels might have
meant by the things he tried to say about moving bodies.

As was also demonstrated in Essay Six in relation to Trotsky's (and
indirectly
Hegel's) attempt to analyse the LOI, Engels's account of motion is
far too vague and ambiguous to be of much use.11a

[LOI = Law of Identity.]

It might be a good idea to remind ourselves what Engels had to
say about motion:

"[S]o long as we consider things as at rest and
lifeless, each one by itself, alongside and after each other, we do not run up
against any contradictions in them. We find certain qualities which are partly
common to, partly different from, and even contradictory to each other, but
which in the last-mentioned case are distributed among different objects and
therefore contain no contradiction within. Inside the limits of this sphere of
observation we can get along on the basis of the usual, metaphysical mode of
thought. But the position is quite different as soon as we consider things in
their motion, their change, their life, their reciprocal influence on one
another. Then we immediately become involved in contradictions. Motion itself is
a contradiction: even simple mechanical change of position can only come about
through a body being at one and the same moment of time both in one place and in
another place, being in one and the same place and also not in it. And the
continuous origination and simultaneous solution of this contradiction is
precisely what motion is." [Engels (1976), p.152.
Bold emphasis added.]

I now propose the following disambiguation of Engels's comments about motion in
order to determine if there is any sense at all to be made of what he concluded
about moving bodies:

This opening set looks more promising.
However, it is worth noting that this clarity has only emerged because of the
introduction of the phrase "change of place", in L5. Unfortunately, if this
expression
succeeds in bringing out what Engels meant it would suggest that change
explains motion, not the other way round. Perhaps this minor difficulty can be
circumvented; again, I will leave that for others to decide.

[Still others, of course,
might wonder exactly how the word "change" could be explicated (given
DM) without an appeal being made to a definition that involved the word "motion"
(a definition, it is worth remembering, that has yet to be attempted by
dialecticians --
Graham Priest excepted, of course). Naturally, the use of the
latter term wouldn't alter the 'truth' of L5, but it would make it eminently circular.]

However, even if this 'niggle' were resolvable, the initial promise
L5-L7 seemed to offer soon evaporates when it is remembered that they
fail to rule
out cases where an extended body might move at a later time, say t2,
but not at t1. That is, B could still be
stationary at t1, and in two different places at once (because it is
an extended object), and at rest with respect to some inertial frame, with the subsequent motion taking place
at t2, not at
t1
-- as we saw above with that car.

It is
no use pointing out that Engels had referred to the "same moment" in which all
this takes place, since we don't know if this same moment is t1
or t2.
Moreover, the
significance of these observations is easily lost, but it
revolves around the fact that Engels's account is compatible with an object
being stationary at t1,
and it is no reply to be told that this object moved later, when we are
still owed a 'dialectical' description of motion that captures its necessary and sufficient
conditions -- not a promissory note that the said object will move at some later
time. Anyway, attempts to capture the necessary and sufficient conditions of the
future predicted or hypothesised motion of this object will only attract the same
objection --
that is, if
L5-L7 were replaced with propositions that simply changed the temporal
variable to t2,
no other adjustments having been being made. This is because in that case questions will only
arise as to why this minor alteration is capable of turning L5-L7 into necessary
and sufficient conditions when the use of t1
had
failed to do so earlier. [L6-L8 below attempt to fix this
unexpected glitch.]

The problem,
it seems, lies with L5, since it fails to connect the motion
it mentions with the same instant recorded in L6 and L7. Hence, the following
emendations are required, it would seem:

L8: A moving body, B, involves a
change of place
only at t1, such that:

L6: B is at
(X1, Y1, Z1) at
t1 and at
(X2, Y2, Z2) at
t1.

L7:
(X1, Y1, Z1)
isn't the same place as
(X2, Y2, Z2).

[L5: A moving body, B, involves a
change of place such that....]

Of course, the same caveats could be applied to later
instants so that such a description captures the movement of the body in question along its entire trajectory. That would merely entail the use of "tk"
in the place of "t1"
in L8 and L6. This complication will be ignored here, since it doesn't
seem to affect the points at issue.

Unfortunately, however, L6-L8 don't appear to imply a contradiction --, that
is, not unless it is clear that B is no
longer at (X1, Y1, Z1) at
t1, since
it is possible for a (stationary) body to be in two places at once. For example, few
would regard it as a contradictory feature of reality that a cake, say,
could be in a box and in a supermarket all at once (hence in two places
at the same time), and stationary with
respect to some inertial frame.

On the
other hand, if a die-hard dialectician could be found who
thought
that the above scenario wascontradictory,
they
would need to explain to the rest of us exactly what this alleged contradiction amounted
to, and
how, in virtue of its being in two such places at once, for example, the cake involved
was
engaged in some sort of 'struggle', and with what it was 'struggling'! As we
will see in Essay Seven Part Three,
the
dialectical classics
inform us that objects turn into their opposites -- that is, they turn into whatever they are contradicted by,
or with what they 'struggle'. In the above example, that would seem to involve this cake
'struggling' with and then turning into the building that housed it! Since no
one in their left mind could reasonably be expected to believe this, cakes in
supermarkets can't be
regarded as in anyway contradicting the bricks and mortar that surround them.
Anyone who still thinks this is advised to seek professional help.

Of course, it could be objected that since
the first location (i.e., the tin) is itself located inside the second
(i.e., the building), the above isn't at all what Engels meant. But, on the
basis of which of Engels's words is that objection itself predicated? Engels
didn't tell us what he meant by "place", so it isn't possible to rule out the
above counter-example because of anything Engels himself said. Indeed, as we
will see later, the word "place" is far more complex than Engels, Hegel, and
even Zeno, acknowledged.

In order to rectify this minor glitch, we need to replace L6 with L9, as follows:

L8: A
moving body, B, involves a change of place
only at t1,
such that:

L9: B is at
(X1, Y1, Z1)
at t1 and not at
(X1, Y1, Z1)
at t1, and B is at
(X2, Y2, Z2)
at t1.

L7:
(X1, Y1, Z1)
isn't the same place as
(X2, Y2, Z2).

[L6: B is at
(X1, Y1, Z1) at
t1 and at
(X2, Y2, Z2) at
t1.]

Now, this set (henceforth, "ℒ")
certainly looks inconsistent. The question, though, is: Can all of its constituent
sentences be false at once? Only if we can rule out that
eventuality is it possible to construct a contradiction from all and only
elements of ℒ.

[At this point it is worth
recalling that a set S of sentences is inconsistent just in case
not all of its elements can be true at once. But, a "contradiction"
requires more than this. In the simplest case, the elements of a binary
sub-set of sentences taken pair-wise from elements of S are contradictory just in
case (a) Those elements are inconsistent and (b) They can't also be false
together. In short, they can't both be true
and they can't both be false.
This salient fact
is invariably overlooked by DM-theorists, which, naturally, leads them into
confusing
contradictions with inconsistencies or contraries -- and, in many cases, with a host of
other unrelated things, too. (Any who
object to the 'pedantry' here should read
this, and
then maybe think again.)]

The question is, therefore:
Can all of the elements of ℒbe false at once? If they
can, then
it won't be possible to construct a contradiction from all and only elements
of ℒ. I propose to resolve this question by considering each ofℒ's
constituent sentences in turn, but in reverse order:

(1) L9 would be false if at least one of its conjuncts was
false. But, the first part of L9 ["B is at (X1, Y1, Z1)"] could be false in several ways: for example, if B
is at (X3, Y3, Z3) at t1.

L9: B is at
(X1, Y1, Z1)
at t1 and not at
(X1, Y1, Z1)
at t1, and B is at
(X2, Y2, Z2)
at t1.

[In fact L9
is an inconsistent sentence anyway, and hence it is false(either
that, or it isn't a proposition to begin with (which is what I would maintain, anyway)11b --, depending on which branch of the Philosophy
of Logic one attends to).
However, since DL is based on the claim that
an inconsistent sentence, or pair of sentences, can be true,
I have ignored this complication because it would
beg the question.]

(2) L8 is linked to L9 by means of a "such that" phrase, so the truth or
falsehood of L8 is sensitive to the truth or falsehood of L9. Hence, when L9 is
false, L8 is, too.

L8: A
moving body, B, involves a change of place
only at t1,
such that:

(3) L7 could be false if (X1, Y1, Z1)
werethe same place as
(X2, Y2, Z2).
This would make L9 false, as well.

L7:
(X1, Y1, Z1)
isn't the same place as
(X2, Y2, Z2).

In which
case, it looks like we can imagine situations in which, while not all of ℒ's elements
could be true at once, all could be false at once. This means that
it isn't possible to construct a contradiction from all
and only elements of ℒ.

Knowledgeable readers will no doubt have noticed the illegitimate way in which
some of the
schematic sentences of ℒ(and others) have been interpreted to derive this
spurious
result. The reason for this ploy (and what its implications are) will be commented uponpresently.

Finally, it could be objected that the above argument is spurious anyway, since
the contradiction to which Engels was referring here is a dialectical,
not a formal, contradiction. This objection has already been considered and
batted out of the park. Readers are, therefore, referred back to that earlier
discussion (here and
here).

From this point on it will be assumed that the difficulties with Engels's
account noted in the previous section (whether or not they are legitimate) can be resolved, and that there exists some way of reading his words that
implies a contradiction, and which succeeds in distinguishing moving from
motionless bodies.

Perhaps the following will suffice?

L10: For some body b, for some time t, and for
two places p and q, b is at p at t and not at
p at t, and b is at q at t, and p is
not the same place as q.

This looks pretty contradictory. With
suitable conventions about the use of variables we could abbreviate L10 a little
to yield this slightly neater version:

L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.

However, one point needs
underlining here: none of the strictures dialecticians impose on the LOI
can be allowed to stand if L11 is to be of any use, otherwise we would lose the ability to talk about
"the same body", "the same time" or "the same place". This would also affect the
application of certain conventions governing the use of terms such as "same
variable", "same meaning" and "same reference". Hence, if we are to depict the
contradictory nature of motion successfully we are forced to accept as valid
the application of the LOI to the use of the same words
and the same variables ranging over temporal instants (but, as a rule of language,
not a
'logical truth' -- why this distinction is important is explained in Essay Twelve
Part One). Since protracted
examples of motion (plainly!) take place over very extended time periods, we can't appeal to the
'relative stability of
language' to fix the reference of these variables (or the reference of
their ordinary language counterparts), if the LOI isn't applicable in all cases.

[FL = Formal Logic; MFL = Modern FL; LOI = Law of
Identity.]

But, if the LOI is rejected then Engels's description would become irredeemably vague.
Many of the 'spurious' objections rehearsed
toward the end of the previous section (in relation to ℒ)
depend on
ignoring some or all of these conventions; as a result they were entirely
illegitimate. Of course, that ploy was deliberately aimed at underlining this
very point: the use of variables in FL is based on conventions that
DM-theorists must themselves observe (in ordinary discourse and in logic) if
Engels's analysis of motion is to be rendered at least minimally comprehensible, but which
conventions in turn undermine their own criticisms of the LOI! Naturally, it is a moot point which horn of this dilemma
dialecticians will want
to "grasp": (i) Accept
Hegel's criticisms of the LOI and thus sink Engels's
analysis of motion, or (ii) Accept Engels's account and reject Hegel's
criticism of the LOI.

It could be objected that the above comments represent a
caricature of the criticisms dialecticians make of the LOI. The relative
stability of both material bodies and linguistic expressions permits
talk about such things as the "same body", "same word", "same place", "same variable",
"same moment", and so on.
Moreover, dialecticians do not flatly deny or reject the LOI; they just claim that it is
true only within certain limits. In addition, they hold that objects and
processes in change possess "identity-in-difference".

These responses are considered in extensive detail in
Essay Six;
the 'relative stability argument', for example, was neutralised
here, here, and
here. 'Dialectical contradictions'
themselves have been analysed in
Note 1 -- as well ashere,
here,
here,
and here.

Of course, hard-nosed dialecticians might choose to ignore MFL
altogether. That is, of course, their right. But, as a consequence of that
unwise decision they would find it rather
difficult to say what Engels actually meant in the quoted passage above. [Anyway, that
rather desperate ploy will also be blocked later on in this Essay.]

Unfortunately, however, even as it stands, and despite the foregoing
considerations (that is, if the contentious claims made
above about the LOI and MFL are, indeed, misconceived, and were withdrawn as a
result), L11
would still fail to be a logical contradiction, and that is because of several more annoying ambiguities.

In fact,
this new batch of vagaries turns out to be far more intractable than
the relatively minor quibbles considered so far.

This new set of equivocations
revolves around the supposed reference of the "t" variable in L11:

L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.

It is always possible to argue
that L11 really amounts to the following:

L12: For some b, during interval T,
and for two 'instants', t1 and t2
[whereboth t1 and t2
are elements of T, such that t2
> t1], and for two places p and q, b is
at p at t1, but not at p at t2,
and b is at q at t2.

[In the above, t1 and t2 are
sets of nested sub-intervals themselves,
which can be put into an
isomorphism with suitably
chosen intervals of
real numbers; hence the
'scare' quotes around the word
"instant" in L12. (Incidentally, t2
> t1
means that t2
is later than t1.)]

Clearly, the implication here is that the unanalysed variable "t" in L11
actually represents a time
interval,T (as opposed to an instant in time) -- which
alternative
was brought out by L12
-- during which the
supposed movement takes place. Plainly, this would licence a finer-grained discrimination
among T's sub-intervals (e.g., t1 and t2) during
which this occurs.12

Two possible translations of L12 in less formal
language might read as follows:

L12a: A body b, observed over the course of a
second, is
located at point p in the first millisecond, and is located at q a
millisecond later.

L12b: A body b, observed over the course of a
millisecond, is located at point p in the first nanosecond, and is
located at q a nanosecond later.

And so on.

[Some might want to argue that the above
would in fact freeze motion, since it speaks about the body in question
being "located" at a certain point at a certain time. If it is located anywhere, it can't
also be moving. That is the point Hegel and Engels wanted to make. This response
will be dealt with in much of the rest of this Essay.]

Indeed, this is how motion is normally
conceived, as change of place in time -- i.e., with time having advanced
while it occurs.

[This
mustn't be confused with what Graham Priest has called "The
Orthodox Account Of Motion", classically
represented in Russell (1937), pp.469-74 -- Priest (2006), pp.172-75.]

If this weren't so (i.e., if L12 is rejected), then L11 would imply that the supposed change
of place must have occurred outside of time -- or, worse, that it happened
independently of the passage of time --, which is either incomprehensible (as
even Trotsky would have admitted, see below), or it would imply that, for
parts of their trajectory, moving objects (no matter how low their speed) move with
an infinite velocity! [This inconvenient consequence was pointed out
earlier.]

L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.

L12: For some b, during interval T,
and for two 'instants', t1 and t2
[whereboth t1 and t2
are elements of T, such that t2
> t1], and for two places p and q, b is
at p at t1, but not at p at t2,
and b is at q at t2.

And yet, how else are we to understand
Engels's claim that a moving body is actually in two places at once? If
that were so, a moving body would move from one place to the next outside of
time -- that is, with time having advanced not one instant. In that case, a
moving body would be in one place at one instant, and it would 'move' to another
place with no lapse of time; such 'motion' would thus take place outside
of time. But, according to Trotsky,
that sort of 'motion' can't exist, for it wouldn't have taken place in time.

Indeed, if this were so, we would lose the right to say that a
moving body was in
the first of these Engelsian locations before it was in the second. That
is because "before" implies an earlier time, which has just been ruled out
in this case. Hence, by a
suitable induction clause, and in relation to the entire trajectory of a body's motion, it
wouldn't be possible to say that a moving body was at the beginning of
its journey before
it was at the end!

[The exact
reasons for saying this will be spelt out in detail
below, but the
above conclusion depends on an argument presented
here, which readers would
be wise to consult first. Trotsky's 'worries' about 'instants' will be
examined again, below. The
contrary idea that if a body is located at a point
at an instant, it must be stationary, will also be examined below.]

Despite this, it might seem that this latest difficulty could be
neutralised by means of a
stipulation
to the effect
that whereas time isn't composed of an infinite series of
embedded sub-intervals (or, rather, our depiction of it isn't) -- given by suitably defined
nested
sub-sets of real
numbers --, location is.

[Once more, such a stipulation would have to reject Trotsky's strictures on
events taking place only in time.]

This would further mean that while we may
divide the space occupied by a body (as it moves along) as finely as we wish -- so that no matter
to what extent we magnify a body's location, we would always be able to
distinguish two contiguous (or proximate) points in its path that allow us to say that
that body was
in both of these places at the same time --, while we can do that with respect to location,
we can't do the
same with respect to time!

Clearly, this is an inconsistent approach to
the divisibility of time
and space -- wherein we are allowed to divide one of these variables (space) as
much as we like, we can't do that with the other (time).

In fact, this is actually where the alleged 'contradiction'
originated; it was introduced into this 'problem' right at the start by this inconsistent (implicit) assumption, so no wonder it 'emerged' at a later
point (no pun
intended).

This
inconsistent protocol might at first sight seem to neutralise an earlier
objection (i.e., that even though a moving body might be in two places, we could
always set up a one-one relation between the latter and two separate instants in
time, because time and space can be represented in an equally fine-grained
manner), but, plainly, it only achieves that result by stipulating (without any justification) that the successful mapping of
occupied places onto
nested intervals of real
numbers (to give them the required density and continuity)
is denied of temporal intervals.

(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not place, or
it is true
of place but not time).

Naturally, these aren't the only alternatives, but they seem to be the
only ones relevant to matters in hand.

Of course,
one particular classical response to this dilemma ran along the lines that the infinite
divisibility of time and place implies that an allegedly moving body is in fact
at rest at some point. Hence, if we could specify a time at which an
object is located at a point in space, and only that point at that time, it must be at
rest at that point at that time. [This seems to be how Zeno, at least, argued --
or, it is at least what his argument implied.]

Nevertheless, it seemed
equally clear to others that
moving bodies can't be depicted in this way, and that motion must be an
'intrinsic' (or even an 'inherent' property)
of moving bodies (that is, we can't depict moving bodies
in any way that would imply they are also stationary), so that at all times a moving body must be in
motion, thus allowing it to be in and not in a given location at one and the same
time. [This seems to be Hegel's view of the matter -- but good luck to anyone
trying to find anything that clear in anything he wrote (about this topic,
or any other)! It is also argued for in Priest (2006).]

If so, one or more of the
above options must be rejected. To that end, it seems that for dialecticians (1) and (3) must be dropped, leaving only (2):

(2) Infinite divisibility is true of location only.

However, it
is important to add that the paradoxical conclusions classically
associated with these three alternatives only arise
if other,less well appreciated (but often implicit), assumptions are either left out of the picture
or are totally ignored
-- that is, in addition to those alluded to above concerning the continuity
of space and the (assumed)
discrete nature of time. As it turns out, the precise form taken by
several of these suppressed and unacknowledged premisses depends on what
view is taken of the supposedly 'real' meaning of words like "motion" and "place".

In Essays Three
Part One
and Twelve Part One, it was
shown that philosophical 'problems' like this arise when ordinary words are
twisted beyond recognition (which criticism, incidentally, was
endorsed by Marx), or
they are put to use in contexts far removed from their ordinary employment. One
or both of these are then compounded when
the
new DM-conventions associated with the use of such terms, which emerge as a result, are
then mis-interpreted as super-empirical truths, and not as misconstrued conventions,
which is what they are.

[The justification for these seemingly dogmatic assertions can't be entered into
in this Essay; I have discussed this topic in extensive detail in Essay Twelve
Part One -- link above.]

In short,
the 'classical' approach to this 'problem' only gets off the ground if linguistic
conventions (or rules) are mistakenly interpreted as Super-Scientific,
Mega-Empirical propositions,
which reflect, or represent, 'industrial strength' DM-facts.

Hence, this approach mistakes
what amounts to a
decision to use words in a novel way, as if they were capable of providing an
'objective' reflection of fundamental truths about reality itself, instead of
their being a vacuous by-product of linguistic tinkering instead.

Indeed,
this is precisely how theorists (in Ancient Greece) began to misread
and misconstrue the products
of social relations (i.e., the aforementioned conventions and rules) as if they were, or
as if they expressed, the real relations
between things, or even were those things themselves -- thus
fetishising
language. Because of this, Traditional Theorists imagined they could 'derive' Super-Theses
like these from
the 'philosophical' jargon they had invented
for that express purpose --,
as the late
Professor Havelock pointed out:

"As long as preserved
communication remained oral, the environment could be described or explained
only in the guise of stories which represent it as the work of agents: that is
gods. Hesiod takes the step of trying to unify those stories into one great
story, which becomes a cosmic theogony. A great series of matings and births of
gods is narrated to symbolise the present experience of the sky, earth, seas,
mountains, storms, rivers, and stars. His poem is the first attempt we have in a
style in which the resources of documentation have begun to intrude upon the
manner of an acoustic composition. But his account is still a narrative of
events, of 'beginnings,' that is, 'births,' as his critics the
Presocratics were to put it. From the standpoint of a sophisticated
philosophical language, such as was available to Aristotle, what was lacking
was a set of commonplace but abstract terms which by their interrelations could
describe the physical world conceptually; terms such as space, void, matter,
body, element, motion, immobility, change, permanence, substratum, quantity,
quality, dimension, unit, and the like. Aside altogether from the coinage of
abstract nouns, the conceptual task also required the elimination of verbs of
doing and acting and happening, one may even say, of living and dying, in favour
of a syntax which states permanent relationships between conceptual terms
systematically. For this purpose the required linguistic mechanism was furnished
by the timeless present of the verb to be -- the copula of analytic
statement.

"The history of early
philosophy is usually written under the assumption that this kind of vocabulary
was already available to the first Greek thinkers. The evidence of their own
language is that it was not. They had to initiate the process of inventing it....

"Nevertheless, the
Presocratics could not invent such language by an act of novel creation. They
had to begin with what was available, namely, the vocabulary and syntax of
orally memorised speech, in particular the language of
Homer and
Hesiod. What they proceeded to do was to take the language of the mythos and
manipulate it, forcing its terms into fresh syntactical relationships which had
the constant effect of stretching and extending their application, giving them a
cosmic rather than a particular reference."
[Havelock (1983), pp.13-14, 21. Bold emphases added; quotation marks altered to
conform with the conventions adopted at this site. Spelling modified to agree with
UK English. Links added.]

As a
result of this ideologically-motivated 'wrong turn' (on that, see below, as well
as
here), Traditional Philosophers
reasoned that the word "motion", for example, really implied some sort
of 'problem', 'contradiction', or 'paradox', which needed to be resolved.
Of course, they imagined they were talking about 'motion itself' and not about the
words we use to talk about it -- or, indeed, about what these words supposedly 'reflected'.
But, as we will see, since they concentrated their
attention on a limited and unrepresentative range of examples, as well as a
severely restricted set of terms associated with this phenomenon (which they also misconstrued), what they
had to say about motion in the end depended on this misconstrual
and on this narrow choice of examples. Indeed, few, if
any, questioned the original distortion, or fetishisation, that had been inflicted on ordinary words
used to describe
movement, location, and change --, which linguistic chicanery had artificially created
these 'philosophical problems', to begin with.
As Keith Thomas
pointed out in relation to 16th
century magicians:

"It would be tempting to
explain the long survival of magical practices by pointing out that they helped
provide many professional wizards with a respectable livelihood. The example of
the legal profession is a reminder that it is always possible for a substantial
social group to support itself by proffering solutions to problems which they
themselves have helped to manufacture." [Thomas (1972), p.295. Bold
emphasis added.]

The same could be said, but
perhaps with even more
justification, about the 'philosophical problems' invented by Traditional
Philosophers.

That is because these thinkers came from those sections of society that were divorced from
the world of
collective labour and communal life, but whose theories reflected an Ideal view
of 'reality' that this privileged life-style motivated. This view of the world
was also
born out of an ideologically-driven denigration and depreciation of the vernacular. [Again, these allegations
will be fully-documented in Essay Twelve (summary
here).]
So, in the view of these 'thinkers', if the
world is ultimately Ideal, it would be quite 'legitimate' to derive
Super-Scientific truths about it from language
or 'thought' alone -- indeed, as we saw George Novack point out
earlier.

The fact
that the classical 'paradox' of motion is based solely on a set of initial
(surreptitious and, as it turns out, illegitimate and unacknowledged)
false
linguistic
moves like this is confirmed by the further fact that the acceptance or rejection of one
or more of the three options listed above (repeated below)
can't be (and has never been) based
on evidenceof any sort. Severally or collectively, each of these
alternatives is founded on linguistic conventions overtly or covertly
accepted by all the parties to this metaphysical con-trick,
conventions
that
appeal to what is supposed to be the 'real'
meaning of the word "motion" -- or, indeed, the 'real' meaning of any of the
other terms associated with it (such as "place", "same", "time"
and "instant") -- to derive paradoxical or 'contradictory' conclusions.

Moreover, the choice of one or more of options (1)
to (3) (as a way motivating a particular, favoured 'solution' to this artificially-created 'problem') also
depends on the acceptance
of one or other of two further ideas:

(A) Even if the specification of the location of a
moving body is in no way problematic (in that we can always and
uncontroversially declare that a moving body is in
two places at once), the specification of the time, or times, when this occurs is.
So, while time can be partitioned as much as we like, location can't.

(B) Even if the specification of the
temporal history of a moving body is in no way problematic (in that we can always
and uncontroversially track a moving body and declare it to be wherever it is a
particular 'moment'), the specification of its location in such moments is
-- in that it is both "here and not here" at some specific time. So,
while location can be divided as much as we like, time can't.

As
far as option (A) is concerned, the identification of point
instants in time represents the heart of the 'problem', while the specification
of points in
space hardly raises a eyebrow. The obverse of this, of course, provides the rationale for option (B).

With respect to DM,
we can see the tension between these two approaches to this 'problem' from the way
that Trotsky, for example,failed to draw the same conclusions about locations
in space that he drew about 'instants' in time. After all, how is it possible to
declare that an instant in time is an abstraction, which can't actually exist, but
fail to say the same about 'locations'? It can't be that objects have to
be somewhere in order to exist, since they also have to be wherever they
are at some time, too.12a If, according to Trotsky, instants in time don't exist
(since they are mathematical fictions), how is it possible for points in space
(that is, mathematical points in space) to exist? If the one can't exist,
how can the other?

Moreover, mathematical points are problematic
in other respects, too: they aren't spherical, nor do they have
any other shape -- otherwise they would have parts and hence wouldn't be
mathematical points. They therefore have no radius or circumference, and so they
can't be 'occupied' by moving bodies -- plainly, they aren't containers or they wouldn't
be points, once more. But, which DM-theorist has ever expressed any
reservations about these obvious facts? Of course, in modern Mathematics and
Physics, these issues are handled differently, where the functional relation
between space and time (with respect to moving bodies) is expressed differently
(in the Calculus, for example); but this can't help us resolve this 'problem'. That is
because (i) It has directly arisen out of age-old linguistic confusion, and (ii) Mathematics
isn't a description of the world. If it were then nature would be Mind. [Why
that is so will be explained in Essay Twelve. I return to this topic again,
below.]

Be this as it may,
it seems reasonably clear that DM-theorists have in general opted for
alternative (B):

(B)
Even if the specification of the temporal history of a moving body is in no way problematic (in that we can always
and uncontroversially track a moving body and declare it to be wherever it is a
particular 'moment'), the specification of its location in such moments is
-- in that it is both "here and not here" at some specific time. So,
while location can be divided as much as we like, time can't.

(1) Both time and
place are infinitely divisible.

(2) Infinite divisibility is true of location only.

(3) Infinite divisibility is true of either (i.e., of time but not place, or
of place but not time).

Nevertheless, (1)-(3) appear to be among the fundamental issues that have
exercised Traditional Philosophers for millennia -- and now dialecticians. In their case, however, the preferred
'solution' appears to rule out the possibility of a moving object being
in two contiguous places
at two different times.
This
means, therefore, that DM-theorists have implicitly opted for alternative (2):

(2) Infinite
divisibility is true of location only.

[With
the word "indefinite" perhaps replacing "infinite", here.]

As has
already been noted, this
choice was motivated by a surreptitious exclusion: the indefinite division of time
is ruled out, while that of location isn't.13

Finally,
but more importantly, the 'solutions' on offer in Traditional Metaphysics (over
the last two millennia) are
similarly based on the rejection of at least
one implication of the ordinary understanding of motion, which
is that moving bodies occupy different places at different times. This is
such a mundane connotation of our everyday grasp of certain kinds of motion that
it seldom features in classical discussions, except perhaps where it is rejected
out-of-hand as far too 'crude'
to be worthy of consideration. [Or it is conflated with the 'Orthodox Account',
mentioned earlier.]

However, as we shall soon see (indeed, as
we will also see in
several other Essays
posted at this site), the protocols of ordinary language and common
understanding aren't so easily
ignored, dismissed, depreciated,
or waved aside.

However, there are and can be no a priori empirical constraints on the length of
a time interval. In fact,
as was noted above, Engels's account of motion was not and
could not have been derived from observation or experiment -- mediated or
not via the naïve or
the sophisticated version of the RTK. Nor could his idea of 'motion in general'
have been materially-grounded, either
--
nor, indeed, could any conception of 'abstract motion'.

[RTK = Reflection Theory of Knowledge.]

That is because human beings -- aided or not by the use of microscopes,
computers, cameras or lasers -- do not possess powers
of discrimination sufficiently fine-grained to allow the study of
movement in the intricate detail required, so that 'reflection' (or 'abstraction') could
be presented with anything useable to work with, or upon, in order to decide
what does or does not happen to moving bodies in an 'instant'. And nor do the
machines or devices we employ.

And, it is little use objecting that this or that
'must' be true of 'motion itself', for that would be to concede the fact that a 'must'
like this had been
derived from the assumed 'real' meaning of a few words, the import of which, as we will soon see,
is far less straight-forward than Traditional Theorists would have us believe.

It
could be countered that
the classical analysis of motion follows deductively from certain incontestable,
if not self-evident,
premises. There are only a handful of possibilities that the world could
conceivably present to us. Engels's analysis, via Hegel, is based on one of these.
If so, what's the
problem?

Once more, the problem
which the above response is
that the deducibility or
otherwise of these conclusions from such premises depends on the use of a handful of words the
meanings of which have been artificially
modified, construed and/or constrained -- such as "place", "move", "time",
and "moment". These words have
either been idiosyncratically, or narrowly, (re-)defined, or they have had their meanings
(implicitly) altered in other ways.
In that case, nothing reliable can follow from their use (as I hope to show
later in this Essay). This was, of course, the point
Marx was trying to make. Indeed, and once again, as George Novack
underlined:

"A consistent materialism cannot proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphasis added.]

But, that is what the
above proffered response achieves; it seeks to derive what seem to be
substantive conclusions about fundamental aspects of the world from "abstract
reason, intuition, self-evidence or some other subjective or purely theoretical
source".

Even worse, not only does nothing legitimately follow from distorted language, it is impossible
to give a clear sense (or any sense) to the classical account of motion (nor, indeed, to more modern versions
of the same that depend upon
this defective tradition). In fact, as will be demonstrated in
Essay Twelve Part One, all
such accounts are non-sensical
and
incoherent; they not only fail to say anything comprehensible
about the world, they
can't.

In that
case, if humanity does in fact possess an
'abstract'
idea of motion (but even this will be contested below,
and in other Essays posted at this site), it can't have been derived
from
'reflection', nor could it have been based on anything ascertainable from the material
world. And these observations become all the more apposite
if it turns out that this 'abstract'
and traditional
idea of motion itself originated from (a) The inequitable
constraint mentioned above -- i.e., that which was arbitrarily imposed on temporal intervals, but excused
of point locations in space --,
for no good reason; and (b) A
ruling-class view of reality.

In
short, Engels's theory wasn't based on reflection (howsoever this 'process' is
understood), or on evidence, or even on 'abstraction', but only on 'concepts' that
were
themselves the product of a series of traditional, or classical,
stipulations and covert conventions -- which were then
imposed
on reality inequitably.

I would be tempting say you just
couldn't make
this stuff
up, but
someone clearly did!

Returning now to re-examine several earlier options; consider L11 and L12:

L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.

L12: For some b, during interval T,
and for two 'instants' t1 and t2
[where t1 and t2
belong to T, t2
> t1], and for two places p and q, b is
at p at t1, but not at p at t2,
and b is at q at t2.

(2) Infinite divisibility is true of location only.

[L12a: A body b, observed over the course of a
second, is
located at point p in the first millisecond, and is located at q a
millisecond later.

L12b: A body b, observed over the course of a
millisecond, is located at point p in the first nanosecond, and is
located at q a nanosecond later. And so on…]

However,
if for some reason L12 were to be rejected as an alternative interpretation of L11
-- that
is, if the idea that time is continuous and indefinitely divisible is flatly denied (even while
this condition is asymmetrically allowed of space); i.e., if
Option (2)
above is simply
imposed on the phenomena
--, then there would seem to be no consistent way of ruling out the
following as yet another alternative:

L13: For some b, for just one instant t, for
three places p1, p2 and p3,
b is at p1 at t, but not at p2
at t, and b is at p3 at t
(where p2
and p3 are proper parts of p1).

Here, a finer-grained discrimination of
position (but not of time) means that L13 isn't contradictory after all;
that is because a body can be
in two places at once whether or not it moves (as we saw
earlier), with no
implication that it both is and isn't in any one of them.14

Translated, L13 could be read
as follows:

L13a: A stationary body b, observed over the course of
an instant, is at
(X1, Y1, Z1) and (X3, Y3, Z3), but not at
(X2, Y2, Z2), where (X3, Y3, Z3)
and
(X2, Y2, Z2)
are both located inside
(X1, Y1, Z1).

L13b: A moving body b, observed over the course of an
instant, is at
(X1, Y1, Z1) and (X3, Y3, Z3), but not at
(X2, Y2, Z2), where (X3, Y3, Z3)
and
(X2, Y2, Z2) are both located inside
(X1, Y1, Z1).14a

[An obvious objection to the above is neutralised in Note 14a
(link above).]

In which case,
this alternative fails to discriminate between
moving and stationary bodies.

An everyday example of L13 might involve a case where a ship, say, enters port;
here the ship could be in the water and in the port at the same time (an,
therefore, extended across several locations,
and hence for it to be in at least two places at once), and be moving, but with no
implication that it is entirely in any one of them at one and the
same instant, or that it is fully occupying any specific part at any moment,
nor yet occupying every point in this finite region (so that it need not
be occupying other areas of that port, for example, at that time). In the latter case,
while it is still inside the said port it wouldn't be in,
say, the dry dock (which is also part of that port),
nor in the staff canteen, or in a host of other places in that port, at that time.

Moreover, the same possibilities would still apply if the ship were stationary with respect to some inertial frame. Here, this ship
could be in one place and not (fully) in it, in two or more places at
once and stationary (or moving), without this implying a contradiction.
Plainly, that is
because this particular example employs a finer-grained division of place to compensate
for the arbitrary imposition of the opposite convention on time.14b

In that case, the alleged contradiction vanishes once again.

[Any who object to my use
of "not (fully) in" here in place of "in" should
read this, and then maybe
think again. I have given a more technical version of this example in Note15.]15

As pointed out above, L12 and L13 may only be
successfully rejected by an ad hoc
stipulation to the effect that while spatial location can be
divided indefinitely, time can't.

But,
even then we have just seen that Engels's half-baked theory still don't work!

In which
case, of course, the allegedly contradictory nature of motion
is at best an artefact of convention -- which only
works by constraining the divisibility of time but not of place. Hence, it isn't
based on 'objective features of reality'.16

Again, it could be objected that no matter how much we partition time, no moving
body can be located at a certain point (i.e., at one point, and one point only)
at that time -- otherwise it would be
stationary.

It could be objected to all
this that while it might not be possible to express the contradictory
nature of motion in ordinary (or even technical) language,17 motion in
the real world must nevertheless be contradictory.18
This might involve the acceptance of one or more of the following (but, so far,
suppressed) assumptions:

L14: An object can't be in motion
and at rest at one and the
same time (in the same inertial frame).

L15: If an object is located at a point it must be at rest at
that point.18a, 18b

L16: Hence, a moving body can't be located
at a point, otherwise it wouldn't be moving, but would be at rest.18b1

L17: Consequently, given L14, a moving body must both occupy
and not occupy a point at one and the same instant.

In which case, it could be argued that L14-L16 (or their 'dialectical' equivalent) capture the
rationale behind Engels's (and even Hegel's) analysis of motion.

Indeed, if this weren't so, it would suggest that motion was either (a)
impossible or (b) illusory --, or even (c) that it was a sort of 'stop-go' affair.18c

As far as (c) is concerned, motion would be
analogous to the way it is depicted in film. There, motion on the screen only appears
to be continuous when it is in fact discontinuous, being composed of
rapidly sequenced 'freeze frames', as it were. When played at a certain speed,
this 'fools' the human eye into 'seeing' continuous movement where there really
isn't any. Given this
'quasi-static' view of motion, if true, a 'moving' body (in the real world, not on film!)
would occupy a point and be stationary at that point, and then occupy another
point an instant later, and be stationary there too, and so on. Naturally, what
the said object gets up to in between such locations at such times would be, on
this view, entirely mysterious. But, on its own, that wouldn't be enough to make this picture of motion false, no
more than certain
quantum
'leaps' (which are discontinuous in this way) would now invalidate QM --
that is, given the way that motion is depicted in Traditional Philosophy.19

[QM = Quantum Mechanics.]

[Options (a)
and (b) above are obviously absurd and won't be considered any further in this Essay
-- although much that is argued later will indirectly reveal just why they
are absurd.]

In order to
reject this 'quasi-static' view (i.e., option (c)), consideration might be given to
one or more of
the following described by Hegel(each defined
in relation to a suitable inertial frame, as necessary). Now, there is no
suggestion that dialecticians have actually argued this way (but, as the
above link shows, Hegel, at least, seems to have had many of these in mind), but what
follows could (plausibly) underpin some of the assumptions and conclusions to
which they might assent (even if only after having read them here for
the very first time!):

L19: If that body subsequently occupies another point, it
must be at rest there, too.

L20: Hence, the above view (and, according to (c)
above) would have us believe that motion is little more than successive
(stationary) pointoccupancy. This means that locomotion must be composed of: (i)
Successive states of instantaneous rest, or (ii) The sequential existence
and non-existence of what only seem to be identical -- but which are in
fact numerically different -- bodies at each of the said points, with 'that body'
falling into non-existence at the end of each instance of location and rest, followed by the
subsequent entry into existence of a new, but seemingly identical body, at the
next moment at the new point, giving only the impression of motion.

[Option (ii) would resemble the way that, say, neon lights in a complex sign can be turned on and off in sequence to create the illusion of motion.
It seems that for a while at least Leibniz held a version of this
theory.]

L21: L20(i) above involves a body in discontinuous motion
separated by periods of instantaneous rest, while L20(ii) involves a body, or series of
bodies, in discontinuous existence at contiguous locations.

L22: L20(ii) must be rejected as absurd.

L23: If L20(ii) is rejected then L20(i) implies that in
between each successive point occupancy a body must pass through an indefinite
(possibly infinite) number of intervening locations.

L24: Hence, even on the assumption that
motion is discontinuous, there will still be an indefinite number of such
intermediate points that a moving object has to occupy while it is passing
between the points at which it is said to be at rest in consecutive instants,
but which intermediate locations the body must both occupy and leave at one and
the same instant. In that case, that body can't be at rest in any of these intermediate points.

L25: Consequently, if motion takes place -- and
it is
either
continuous or discontinuous -- a moving body must both be located and not
be located in a given place at one and
the same time, namely at these intermediate points, at the very least.

L26: Therefore, the assumption that a body is in motion
only
if it occupies and is at rest in successive locations at contiguous instants is
false -- for even on that assumption, a body must violate this condition for an
indefinite number of intermediate points between each successive instance of 'rest', at
successive instants.

L27: Therefore, either motion is impossible or
illusory (which is absurd), or motion can't be wholly discontinuous.

[It is possible to strengthen L27 by
means of L27a, but that option won't be pursued further here:

L27a: Therefore, either motion is impossible
or illusory (which is absurd), or motion can't be discontinuous.]19a

However, it is worth noting that the
above argument begins with the rejection of an apparent contradiction --
expressed in L14 (restated below, but
re-numbered
L28, and hence very slightly modified) alongside its supposed contradictory, L29:

L28: A body can't be at rest and in motion at the same time
in the same inertial frame.

L29: A body can be at rest and in motion at the same time
in the same inertial frame.

Naturally, that depends on whether these are genuine contradictories; I will
ignore this minor complication in what follows. On the other hand, if they aren't even
propositions, then they can't be contradictories to begin with.
Nevertheless, I
will assume they are propositions for the purposes of this argument;
however, their status as
propositions will be questioned in Essay Twelve Part One.20

If
these 'niggles' are now put to one side,
then L29 is true if L28 is false, and vice versa.

As is well-known, an analogous series of
background assumptions motivated Zeno into
trying to
'prove' that motion was either impossible or illusory. DM-theorists clearly
reject Zeno's conclusion, but it seems they can only do so by accepting
L28 (or its equivalent), thus rejecting L29, in order to derive their own contradiction expressed in L17,
which was:

L17: A moving body must both occupy and not occupy a
point at one and the same instant.

Plainly, if
L28 were false (and L29 true) -- which would mean that a body could be moving
and at rest at the same time --, L17 might not look quite so compelling.
At any rate, it is clear that dialecticians have to reject one 'contradiction' (expressed
in L29) in order to derive their own (in L17).

L28: A body can't be at rest and in motion at the same time
in the same inertial frame.

L29: A body can be at rest and in motion at the same time
in the same inertial frame.

[It
could be argued that the contradiction in L29 isn't dialectical. But, as we have
seen (here and
here), the
'contradiction' Engels and Hegel claimed to have found in motion isn't
dialectical either. On that see Note 18a.]

Now, when
L17 is conjoined with L28 we obtain the following:

L17a: Since a body can't be at rest and moving at one and the
same time in the same inertial frame, a moving body must both occupy and not
occupy a point at one and the same time.

This seems to be the 'contradiction' that exercised Engels. If
so, it is worth asking: Which of the following two 'contradictions' is it
legitimate to accept or reject: L17 or L29?

L17: A moving body must both occupy and not occupy a point at
one and the same instant.

L29: A body can be at rest and in motion at the same time
in the same inertial frame.

Which of these
'contradictions' is the
more absurd? If L29 were true, L17a couldn't be derived in any
obvious way fromL14-L27. This would in turn mean that Engels's
conclusion is false
--
always assuming, of course, that his 'argument' depends on such considerations
and some sense can be made of anything he had to say on this topic.

Nevertheless, it is clear
from the way that the above argument has been constructed that L17a itself
depends on the truth of L28:

L28: A body can't be at rest and in motion at the same time
in the same inertial frame.

L17a: Since a body can't be at rest and moving at one and the
same time in the same inertial frame, a moving body must both occupy and not
occupy a point at one and the same time.

[L14: An object can't be in motion
and at rest at one and the same time (in the same inertial frame).]

That is because L14-L27 began
with the assumed truth of L14 -- or, its equivalent, L28. The reverse
implication doesn't appear to hold.

[It is impossible for me to say whether or
not the reverse implication holds; all I am trying to do here is make sense of the idea that motion
is contradictory, and this seems to be the only way to do that. Again, since
DM-theorists refuse to be clear what they mean on such issues, it has been left to me to try
to make sense of what they do allege.]

This
means that L28 doesn't seem to pre-suppose
the truth of the conclusion drawn in L17a, whereas the conclusion drawn in L17a looks like it depends on L28. This in turn suggests
that L28 might be the more fundamental of the two.

L17a: Since a body can't be at rest and moving at one and the
same time in the same inertial frame, a moving body must both occupy and not
occupy a point at one and the same time.

Be this as it
may, L28 is itself false if L29 is true:

L28: A body can't be at rest and in motion at the same time
in the same inertial frame.

L29: A body can be at rest and in motion at the same time
in the same inertial frame.

Unfortunately, L29 is a familiar
truth! An object can be at rest with respect to one inertial frame, and
yet be in motion with respect to another. The wording of L29 doesn't
rule this out. In order to eliminate this latest difficulty, L29 must be
modified; perhaps along the following lines:

L30: With respect to the same inertial frame and the
same instant in time, a body can be at rest and in motion.

It is
worth noting that L30 'contradicts' L30a:

L30a: With respect to the same inertial frame and the
same instant in time, a body can't be at rest and in motion.

L30 now certainly looks 'contradictory'
-- especially if the phrase "at rest" is taken to mean "not in motion with respect to the
same inertial frame".

Nevertheless, it was the rejection of L30 (or its equivalent) that led to the
derivation of L17a. Hence, if L30 is always false (i.e., if L30a is always
true), it looks like L28 must always be true, too (given certain other assumptions, and if
worded appropriately).

L17a: Since a body can't be at rest and moving at one and the
same time in the same inertial frame, a moving body must both occupy and not
occupy a point at one and the same time.

L28: A body can't be at rest and in motion at the same time
in the same inertial frame.

Consequently, if we deny that a body can be at
rest and moving at the same time (in the manner indicated above), Engels's conclusion
does appear to follow!

That much seems reasonably clear.

Unfortunately, however, the following line of argument also shows that the
derivation of L17a from the rejection of L30 isn't inevitable, and hence that
Engels's conclusion doesn't automatically follow:

L31: A body can't be at rest and in motion with respect to
the same inertial frame at the same time.

L32: If a body is wholly located at a
point it can't
be wholly located at any other point in the same reference frame at the same
time.

L33: But, a moving body must be located
wholly at two points
at the same time, otherwise it would be at rest.

L34: Since L33 is impossible (by L32),
motion
can't take
place. Hence, by L31, and despite appearances to the contrary, all bodies are at
rest!

Of course, L34 is somewhat analogous to the
conclusion Zeno himself drew, and it flatly contradicts experience. It is
therefore unacceptable -- that is, if we allow experience to be decisive in
such cases. But, L31-L34 demonstrate that L17a doesn't have
to follow from the rejection of L30, even if the alternative outcome proves
unpalatable.

L30: With respect to the same inertial frame and the
same instant in time, a body can be at rest and in motion.

It is now clear that the
refusal to accept the 'contradiction' contained in L30 can lead to two
distinct 'contradictory' conclusions. One of them is inconsistent with
experience (the latter half of L34 -- i.e., L34b), while the other (i.e., L17a) is self-contradictory:

L17a: Since a body can't be at rest and moving at one and the
same time in the same inertial frame, a moving body must both occupy and not
occupy a point at one and the same time.

Naturally, which one of the above two
outcomes proves to be the least unacceptable will depend on other
priorities. If it is felt that experience is unreliable, L34b might be
preferable. On the other hand, if contradictions are regarded as fundamental
features of reality,
L17a might well be chosen. However, it is worth noting that neither option is
empirically verifiable; in fact they both transcend any
conceivable body of evidence and every possible deliverance of experience.21

Of course, it could be argued that L32 begs
the question, since, with respect to moving bodies, DM-theorists claim bodies
can wholly be located at two points at once. In fact, they (L32 and L32)
both beg each other's question.

Nevertheless, given the fact that dialecticians also believe that
appearances contradict underlying 'essences', they are the last ones who can legitimately appeal to experience to refute Zeno-esque conclusions like L34b. In fact,
if the DM-thesis that underlying 'essences' 'contradict' appearances were itself
true, then, since
it appears to be the case that there are moving bodies, in 'essence' the opposite
must be the case! Hence, if appearances 'contradict' reality it seems that, essentially,
no bodies actually move --
which, unfortunately implies that Zeno was right all along!

Putting this annoying corollary to one side for now, it is
important to note that both of the above two 'derivations' rely on the sorts of
ambiguities we encountered earlier with respect to L1-L13 -- alongside several others
to be considered below. As we will see, traditional, aprioristic 'arguments' like these only seem to work because they are shot-through with equivocation,
ambiguity,
and distortion. Indeed,
that is partly why both of the above conclusions finally descend into
absurdity and incoherence -- as we are about to discover.

[Apologies are owed in advance to the reader: the next few sub-sections are
somewhat involved and technical, but there is no other way to expose how
confused the DM-view of motion actually is than this.]

The absurdity in L34b
(below) is quite plain for all to see and needn't detain us any
longer. However, the ludicrous nature of L17a
isn't
perhaps quite so obvious.

L34b: Despite appearances to the contrary, all bodies are
at rest.

L17a: Since a body can't be at rest and moving at one and the
same time in the same inertial frame, a moving body must both occupy and not
occupy a point at one and the same time.

The ludicrous nature of L17a may
nevertheless be made more explicit by means of the following argument -- first
of all assuming the truth of L15b (also assuming "moment in time" is well
understood -- or at least as well understood as it is when Engels used terms
like this):

L15b: If an object is located at a point
for at least two moments in time it must be at rest at
that point.

L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same moment.

L36: Let A be in
motion and at
(X1, Y1, Z1), at
t1.

L37: L35 implies that A is also at some other
point -- say,
(X2, Y2, Z2)
--, at
t1.

L38: But, L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1;
hence it is also at (X3, Y3, Z3),
at t1.

L39: Again, L35 implies that A is at
(X3, Y3, Z3)and at another place at
t1;
hence also at (X4, Y4, Z4), at
t1.

L40: Once more, L35 implies that A is at (X4, Y4, Z4)and at another place at
t1;
hence also at (X5, Y5, Z5), at
t1.

By n successive applications of L35 it is
possible to show that, as a result of the 'contradictory' nature of motion, A
must be everywhere along its trajectory if it is anywhere, and all at t1!22

In summary form, the argument goes as follows:

According to L15b, if A is located at any of the above
points for at least two moments in time (howsoever brief), it can't be moving
but must be at rest. So, if A is located at (X2, Y2, Z2)
for two of thee moments, it must be at rest there. On the other hand, if A
is still moving it can't be located at (X2, Y2, Z2)
for any length of time,but must be somewhere else at the same moment
that it arrived there. If so it must also be at (X3, Y3, Z3)
at the same moment, otherwise it will have stopped moving. The rest
follows as indicated above: A must be everywhere along its trajectory at
the same moment, if it is moving at any point along that trajectory.

But, that is even more absurd than L34b!

L34b: Despite appearances to the contrary, all bodies are
at rest.

The only way to avoid such an outlandish conclusion would be to maintain that L35
implies that a moving body is in no more than two places (i.e.,
less than three places) at once. But, this doesn't help, for, as noted
above, if a body is
still moving and in the second of those two places, it couldn't be in motion at this second location unless it were
in a third place at the very same time -- by L15b and L35.

L15b: If an object is located at a point
for at least two moments in time it must be at rest at
that point.

L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same
moment.
[Emphasis added.]

Once again, just as soon as a body is
located in any one place for any length of time it is at rest
there, given this rather odd way of viewing things. Without L15b (and hence L35), Engels's conclusions
simplydon't follow. So, on this view, if a body is moving, it has to occupy
at least two points at once,
or it will be at rest. But, that is precisely what creates the above
absurdity, for if that body is located at the second of these two points, it must be at
rest there --
unless it is also located at athird point at the same time.

This itself follows from L17 (encapsulated in L17b):

L17: A moving body must both occupy and not occupy a
point at one and the same instant.

L17b: A moving object must occupy
at least two
places at once.

Of course, it could be argued that L17b is in fact true of the
scenario depicted in L35-L40 -- the said body
does occupy at least two places at once namely
(X1, Y1, Z1) and (X2, Y2, Z2).
In that case, this line-of-argument is misconceived.

Or, so it might be maintained.

[The
following remarks are intended for those not too familiar with phrases like "at most two" or
"at least two": if we remain in the
set of positive integers, "at most two" means the same as "less than three"
(i.e., "two or less"), while "at least two" means the same as
"more than one" (i.e., "two or
more").]

The above objection would
indeed be misconceived if Engels had managed to show that a body can only be in
at most two (but not in at least two) places at once, which he not only failed to do,
he couldn't
do.

L17c: A moving object must occupy at most
two places at once.

That is because, between any two points there is a third point, and if the
said body is in
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1then
it must also be in any point between
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1--,say,
(Xk, Yk, Zk).
But, as soon as that is admitted, a moving body must be in more than
two places at once -- namely
(X1, Y1, Z1),
(Xk, Yk, Zk),and (X2, Y2, Z2),
at t1, there seems to be no way to avoid the
conclusion drawn above: if a moving body is anywhere, it is everywhere in its
trajectory at the same time.

[And that is
whythe question
was posed earlier about
the precise distance between the points at, or in, which Engels argues a body performs
such 'contradictory' miracles.]

Putting this annoying technicality to one side for now, it would be unwise to argue that Engels believed this (or
even that DM requires it) -- that is, that a moving body occupies at most two points
at the same time -- since, as we have seen, if that body occupies the second of
these two points, it would be at rest at that point unless it also occupied a
third point at the same time. Given L15b (reproduced below), there seems to
be no
way to circumvent this.

L15b: If an object is located at a point
for at least two moments in time it must be at rest at that point.

On the other hand, a combination here of an "at least two places at once"
with and an "at most two places at once" would be the equivalent of an "exactly two
places at once".

L17d: A moving object must occupy
exactly two
places at once.

However, any attempt to restrict a moving body to
the occupancy of exactly two places at once would only work if that body came to rest at the second of
those two points! L15b says quite clearly that if a body is located at a
point (even if this is the second of these two points) for any period of time,
it must be at rest at that point. In that case, this escape route will only work
if DM-theorists reject their owncharacterisation of motion,
partially captured by L15b.

In that case, if L15b
is still held true, then at the second of
these two proposed DM-points -- say, (X2, Y2, Z2)
--, a moving body will still be moving, and hence it will be in and not in
that second point at the same instant, too.

It is worth
underling this conclusion: if a body is located at a second point -- say, (X2, Y2, Z2)
--, at
t1,
it will be at rest there at t1, contrary to the assumption
that it is moving. Conversely, if that body is still in motion at t1,
it must be elsewhere also at t1,
and so on. Otherwise, the condition that a moving body must be both in a certain place
and not in it at the very same moment will have to be abandoned. So,
DM-theorists can't afford to accept L17d.

L17d: A moving object must occupy
exactly two
places at once.

Consequently, the unacceptable outcome --, which holds that as a result of the
'contradictory' nature of motion, a moving body must be everywhere along
its trajectory, if it
is anywhere, at the same time -- still follows.

Again, it could be objected that when body A is in the second
place at the same instant, a new instant in time would begin. So, while
A
is in (X2, Y2, Z2)
at t1, a
new instant, say t2,
would start.

To be sure, this ad hoc amendment avoids the disastrous implications
recorded above. However, it only succeeds in doing so by introducing
several serious problems of its own, for this
option would mean that
A
would be in (X2, Y2, Z2) at
t1
andt2,
which would entail that A was located in the same place at two different times,
and that in turn would mean that it was stationary at that point! That is
why 15b was introduced earlier.

L15b: If an object is located at a point
for at least two moments in time it must be at rest at that point.

It could be objected, once more, that A-like objects
do in fact occupy two places at once, namely
(X1, Y1, Z1) and (X2, Y2, Z2),
so the above argument is defective. So, the 'derivation' that
purports to show that a moving body must be everywhere along
its trajectory, if it is anywhere at the same time, can't succeed.

We can perhaps clarify this
proffered objection by means of the following:

L38: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X3, Y3, Z3)
at t1.

[L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same moment.]

The idea here is that if we select, pair-wise, any two
points that a body occupies in any order (either
(X1, Y1, Z1) and (X2, Y2, Z2),
or
(X1, Y1, Z1) and (X3, Y3, Z3)..., or
(X1, Y1, Z1) and (Xn, Yn, Zn),
and so on), then L17c will still be satisfied (and the above 'derivation' --
that a moving body must be everywhere along
its trajectory, if it is anywhere at the same time -- fails):

The 'DM-reply' proffered above held that Engels only needed a body to be in any two
places at once -- that is, any two places So, any two places will do. . But, the third place above -- (X3, Y3, Z3)
-- isn't implied by his description of the
'contradiction' involved. L38 (repeated below) only works by ignoring the fact that the
other place in which A is located is precisely
(X1, Y1, Z1);
so, it can't be
in(X3, Y3, Z3) at that time.So, when A is in (i)
(X1, Y1, Z1)
and (X2, Y2, Z2), and (ii)
(X1, Y1, Z1) and (X3, Y3, Z3), and so on, it can't be in at most two places at once, since it is in this case in more than
two. The use of "and" scuppers this line-of-defence.

L38: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X3, Y3, Z3)
at t1.

[L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same moment.]

It could be objected that the above response only works because
an "and" has been surreptitiously substituted for an "or". The original
proffered response in fact argued
as follows:

R1: If we select pair-wise any two
points a body occupies in any order (either
(X1, Y1, Z1) and (X2, Y2, Z2),or
(X1, Y1, Z1) and (X3, Y3, Z3)...,or
(X1, Y1, Z1) and (Xn, Yn, Zn),
and so on), then L17c will be satisfied.
[Bold and underlining added.]

[L17c: A moving object must occupy at most
two places at once.]

But not:

R2: If we select pair-wise any two
points a body occupies in any order (i.e., (a)
(X1, Y1, Z1) and (X2, Y2, Z2),and(b)
(X1, Y1, Z1) and (X3, Y3, Z3)...,and (c) ((X1, Y1, Z1) and (Xn, Yn, Zn),
and... (d)...,
and so on), then L17c will be satisfied.

Unfortunately, once more, this reply simply catapults us back to an earlier
untenable position, criticised above along the following lines:

[B]etween any two points there is a third point, and if the
said body is in
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1 then
it must also be in any point between
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1--, say,
(Xk, Yk, Zk).
But, as soon as that is admitted, a moving body must be in more than
two places at once -- namely
(X1, Y1, Z1),
(Xk, Yk, Zk) and
(X2, Y2, Z2),
at t1, there seems to be no way to avoid the conclusion drawn
above: that if the body is anywhere, it is everywhere in its trajectory at the same time.

In that case, the reply encapsulated in L38/R1 fails, too. So, if a
body is in
(X1, Y1, Z1)
and (X2, Y2, Z2)
at t1, it
must also be in at least one of the intermediate points -- say,
(Xk, Yk, Zk)
--,
also at t1.
Hence, R2 is still a valid objection.

In order to see this, a few of the subscripts in R2 need only be
altered, somewhat as follows:

R3: If we select pair-wise any two
points a body occupies in any order (i.e., (a)
(X1, Y1, Z1) and (X2, Y2, Z2),and(b)
(X1, Y1, Z1) and (Xk, Yk, Zk), and (c)
(X1, Y1, Z1) and (Xi, Yi, Zi)...,
and so on), then L17c won't be satisfied.

It is surely philosophically and
mathematically irrelevant whether we label such
points with iterative letters (i.e., "k" or "i") or with
numerals ("1", "2" or "3"). [Recall, the variables labelled with iterative letters
(i.e., "k" or "i") are intermediate points.]

In which case, R3 implies that if a body is in, say,
(X1, Y1, Z1)
and (X2, Y2, Z2),
at t1, it
must also be in at least one of the intermediate points -- say,
(Xk, Yk, Zk)
--, at the same moment. R3 thus implies that L17c is false.

Moreover, it is also worth asking
the following
in relation to L38: Is A at
(X2, Y2, Z2), at t1?
If it is, then it must be elsewhere at the same time, or it will be stationary.
So much is agreed upon. In that case, the only way to stop the absurd induction
(i.e., the one that derived the conclusion that if a moving body is anywhere it
must be everywhere at the same time) would be to
argue as follows:

L38a: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X1, Y1, Z1),
at t1,
but not at (X3, Y3, Z3),
at
t1.

[L38: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X3, Y3, Z3),
at t1.

L35: Motion implies that a body is in one place
and not in it at the same time; that it is in one place and in another at the
same moment.]

However, this 'straw', once
clutched, has unfortunate consequences that desperate dialecticians might want
to think about before they claw at it too frantically:

L38b: If A is at
(X2, Y2, Z2)
and (X1, Y1, Z1),
at t1,but not at (X3, Y3, Z3),
at t1,
then it must be at (X3, Y3, Z3), at
t2.

L38c: If so, A will be at two places --
(X2, Y2, Z2) and (X3, Y3, Z3)
-- at different times (i.e.,
(X2, Y2, Z2),
at t1,
and (X3, Y3, Z3),
at t2).

L38d: In that case, between these two locations
(i.e., (X2, Y2, Z2)
and (X3, Y3, Z3)), the motion
of A will cease to be contradictory -- since it will not now be in
these two places at the same time, but at different times.

Finally, and perhaps more importantly, the above objection also
falls foul of an earlier response -- that is, that if a moving object is in at most two
places at once, it must be stationary at the second of these two locations.

That becomes clear as soon we re-examine
above objection more closely -- i.e., that A-like objects
occupy two places at once, namely
(X1, Y1, Z1) and (X2, Y2, Z2),
att1.
The question now is: At what point in time does A move from (X2, Y2, Z2) to (X3, Y3, Z3)?
If it does so at t1,
that would mean A occupies more than two points at once -- namely,
(X1, Y1, Z1), (X2, Y2, Z2)and (X3, Y3, Z3),
at t1
-- and the above objection would fail. On the other hand, if A moves
from (X2, Y2, Z2) to (X3, Y3, Z3)
during t2,
then it will be clear that A will
have been located at (X2, Y2, Z2)
for two moments in time, namely,t1
andt2,
and that in turn would mean A was stationary while it is at (X2, Y2, Z2).

So, it seems that dialecticians can only escape from
the absurd consequence of their theory -- that a moving object is everywhere
along its trajectory at
the same time -- by abandoning their belief in the contradictory nature of
motion at an indefinite number of intermediate locations in its transit
(for
example, right after it
leaves the first pair of the places it
occupied in that journey, since it would be stationary at each such point),
thus admitting that the said object was stationary at every point along its
trajectory.

It now looks like DM-theorists' only way
of avoiding the above criticisms -- and of maintaining their view that motion is
'contradictory' -- is if they are prepared to impose a series of ad hocstipulations on nature (of the sort mentioned
above), none of which seem to work,
anyway!

But, as we have seen
several times already, such a response would be fatal to DM in another sense,
too --, since it would
undermine their belief that reality itself is contradictory (rather than
it merely being the result of what we say about it that is), all the while confirming the
suspicion that it is only certain ways of representing nature that
appear to imply it is contradictory --
which "ways of representing nature", incidentally, still await clarification
-- and which don't work, anyway.

This option would, of course, mean that this
core DM-theory is thoroughly conventional, and thus entirely
subjective -- and still defective!

Once again: As we will see throughout
this site, the source of these (and similar) 'problems' lies in the repeated
attempt made by dialecticians (and metaphysicians alike) to state, or derive,
'necessary truths' about reality. Such theses are based solely on an extrapolation
from the supposed meaning of a few specially-selected words to fundamental
truths about nature, valid for all of space and time. Clearly, with
respect to Engels's 'analysis' of motion, this predicament was further compounded
by his attempt to circumvent several fundamental conventions expressed by our use of
ordinary language --, such as those expressed in, or by, the LOC and the LOI.

[I will
endeavour to substantiate these claims below, and in detail in Essay Twelve
Part One.]

It could be replied that the above criticisms
beg the
question, since dialecticians don't question the application of principles drawn
from FL -- such as the LOC --, they merely point to their limitations when
confronted with change and motion. That response was neutralised in Essays
Four and Eight Parts One,
Two, and
Three.

Suffice it to say that dialecticians themselves have yet to account for motion in
anything like a comprehensible fashion -- or even depict it accurately! So,
whether or not it is correct to say that FL can't account for motion and change, it is now quite clear that
DL
itself miserably fails in this regard.

Even more annoying:
as we saw in
Essay Four, and
contrary to what dialecticians tell us, FL copes with
motion and change with relative ease.

Another, perhaps less well appreciated consequence of the
'dialectical theory' of motion and change -- which is, if anything, even more absurd than the one
outline above --, is the following:

If Engels were correct (in his characterisation of motion and
change), we would have no right to say that a moving body was in the first
of these 'Engelsian locations' before it was in the second.

L3: Motion involves a body being in one place and
in another place at the same time, and being in one and the same place and not
in it.

That is because such a body, according to Engels, is in both
places at once, so it can't be in one of them before it was in the
second.

Now, if the conclusions
drawn in the
previous section are valid
(that is, if dialectical objects are anywhere in their trajectories, they are
everywhere all at
once), then it follows that no moving body can be said to be anywhere
before it is anywhere else in its entire journey! That is because such
bodies are everywhere all at once. Hence, they can't be anywhere first and then
later somewhere else. In the dialectical universe, therefore, when it comes to motion
and change, there is no before and
no after -- nor is there any during or while!22a

In that case, according to this 'scientific theory', concerning
the entire trajectory of a body's motion, it would be impossible to say it was at the beginning of its journey
before
it was at the end! In fact, it would be at the end of its journey at the same
time as it set off! So, even though you might foolishly think, for example, that
in order to go on your holidays, you have to board an aeroplane before you disembark at your
destination, this 'path-breaking' theory, DM, tells us you are sadly mistaken: you
not only must get on the plane at the very same
moment as you get off it at the 'end',
in fact you do!

And the same caveat applies to the 'Big
Bang'. While benighted, non-dialecticians might think that this event took
place billions of years ago, they are surely mistaken if this 'super-scientific'
theory is correct. That is because any two events in the entire history of the universe
must have taken place at the same instant, by the above argument. Naturally,
this means that as you, dear reader, are reading this, the 'Big Bang' is in fact
is now taking
place! I rather think 'Duck
and cover!' is called for, here.22b

To be sure, this is absurd, but,
hey, that's Diabolical Logic for
you!

Several of the points raised above require further elaboration -- in the
course of which we will discover once again that Engels
was in fact saying nothing at all intelligible.

As we have seen, Engels asserted the following:

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Engels (1976), p.152.]

However, in doing so he was clearly appealing to what he regarded as the
established, inter-subjective meaning of terms like "motion", "change", "place",
"moment", and "time". This can be seen from the fact that he didn't even think
to define or explain what he meant by these words.

Engels did offer an aside (in the above
comment) to the effect that motion is a "simple mechanical change of place", and
idea he reiterated in DN:

"All motion is bound up with some
change of place, whether it be change of place of heavenly bodies,
terrestrial masses, molecules, atoms, or ether particles. The higher the form of
motion, the smaller this change of place. It in no way exhausts the nature of
the motion concerned, but it is inseparable from the motion. It, therefore, has
to be investigated before anything else." [Engels
(1954), p.70. Italic emphasis added.]

Ordinarily, this lack of precision wouldn't
in itself be a problem since we understand words like these perfectly well in
our day-to-day affairs, and typically without recourse to definitions, etc. But,
in specialised areas -- especially those associated with some attempt to revise or correct
the way we understand or even see things --, a sloppy approach to theory isn't just unacceptable, it is
counter-productive. Indeed, this
cavalier attitude to ordinary language has a tendency to backfire on anyone foolish enough
to adopt it. Again, this is especially true of those who try to press
the vernacular into service way beyond its prosaic remit.

The
ability to manoeuvre one's way around linguistic conundrums like this with ease is
supposedly what dialecticians mean by "grasping a contradiction".
This seems to imply that when confronted with the many 'contradictions' that
nature allegedly throws our way, dialecticians merely have to "grasp" them, and
all is well. This neat trick then 'allows' these 'serial graspers' to ignore the
internal contradictions this approach introduces into their own theory. [The
fatal problems this introduces have been exploredhere andhere.]

However, as we will see in Essay
Seven (and
here), DM-theorists are
highly selective about which 'contradictions' they choose to "grasp",
which they simply drop (or ignore), and which
they try to blame on the defective nature of a rival theory. Hence, when
dialecticians "grasp" the 'contradictions' they claim to see in motion and
change, they attribute them to nature itself -- failing to blame them on Hegel's
logical incompetence,
on Engels's lack of clarity, or, indeed, on Zeno's confused musings.

On the other hand, when contradictions are
detected in rival theories, they become a
handy excuse for berating their inventors, and hence, for rejecting them
root-and-branch. By
way of contrast, they are remarkably forgiving and accepting of the contradictions implied by
their own ideas, which aren't allowed, under any circumstances, to suggest their theories
are defective or in need of revision.

So, for example, they tell us that by 'resolving'
certain contradictions science is able to progress. However, if science advances
by rejecting or 'resolving' contradictions in and between theories, then, plainly, the science of kinematics can't advance unless this
'dialectical contradiction' has also been resolved (as, indeed, it will be
by the end of this Essay --, except it will be done by dissolving it).
However, just as soon as that has been done, dialecticians
will surely have to abandon their belief in the 'contradictory' nature of
motion, or, of course, risk holding up the progress of science.

As seems obvious, 'dialectically grasping' a 'contradiction'
doesn't make it disappear. Even if we grant for the moment the veracity
of DM, motion is still
'contradictory', whether or not anyone else sees things this way. Hence, the
significance of
"grasping a contradiction" appears to be little more than this:
Certain processes in nature and society, which might
seem puzzling or paradoxical (to some), suddenly stop bothering
dialecticians -- that is, if ever they did concern them. But, this only works if it is accepted
that this is the way the world actually is. In that case, and
on this basis, DM-theorists seem to think they can stop worrying about the
contradictions their world-view places at the heart of their own theory. They
accept the fact that even though nature is deeply perplexing, a pair of
well-adjusted DM-spectacles allows the world to be viewed aright (where
"viewed aright" in fact appears to mean "ignore what you can't explain and
then accuse critics of not understanding dialectics").

Despite the
DM-spin, this nevertheless implies that it is impossible to
explain what it could possibly mean for something to be in two different
places at once
(save in the ambiguous manner described earlier in this Essay, and again below).
If that is so, the dialectical 'analysis' of motion is of little use to
anyone, least of all to dialecticians. That is because it is clear that not even
dialecticianscan explain motion, since all that their theory does is re-describe it in a perplexing
form. All that Engels's 'analysis'
seems to have achieved, therefore,
is stopping dialecticians worry about their own defective theory, leaving
motion, as they see it, still a 'paradox'.

We
have also seen that, even if DM were a correct description of 'reality',
this view of motion does no real work. How does it help us change the
world to be told that motion is contradictory? How does it help scientists to be
told motion is a contradiction? Can they use it to predict anything? Can
technologists and engineers use it to help control nature? How many bridges can
be built on the basis that motion is a contradiction? How many strikes won? Or
even leaflets printed? What dialectical use is it?

In that case, if there isin
fact a rational solution
to this 'paradox' -- if we but knew what that was --, it is no good looking to dialecticians
for an answer. They gave up on that
score the moment they leafed through Hegel's 'Logic', and began "grasping"
'contradictions'.

Left to DM-fans, the advancement this branch of Physics and Applied
Mathematics would come to a grinding halt.23

However, Engels did at least make an attempt to use everyday terms in his
effort to show that they were not all they seemed -- or, rather, that when
considered 'dialectically' the vernacular reveals more about reality than might
otherwise have been apparent, especially to those who
are mesmerised by
'commonsense' and 'formal thinking'. Or, indeed, those who have been bamboozled by that 'inner
fifth-columnist', the "abstract understanding"
(very helpfully identified for us by Hegel without the use of a consulting
couch or even a brain scan).

Nevertheless, anyone who disagreed with the 'dialectical'
conclusions Engels drew would no doubt be reminded that these few words -- or,
the 'concepts' they supposedly represented -- clearly and unambiguously implied the
'contradictions' that Engels and Hegel said they did. In that case, defenders of
the 'dialectical view' of things could claim that Hegel and Engels had actually
made explicit what were in fact implicit
'contradictions'.

Intentionally or not, by arguing this way Engels
succeeded in situating his paradoxical theses in an ancient metaphysical tradition
stretching back to Zeno,
Parmenides and
Heraclitus -– a tradition which
ordinary working people had no hand in building, but which is (demonstrably) based on ruling-class
priorities,
forms-of-thought, and,
not uncoincidentally, on a distortion of the
vernacular, the
only language that links humanity directly with the material world, as Marx
himself pointed out:

"One of the most difficult tasks
confronting philosophers is to descend from the world of thought to the actual
world. Language is the immediate actuality of thought. Just as
philosophers have given thought an independent existence, so they were bound to
make language into an independent realm. This is the secret of
philosophical language, in which thoughts in the form of words have their own
content. The problem of descending from the world of thoughts to the actual
world is turned into the problem of descending from language to life....

"The philosophers have only
to dissolve their language into the ordinary language, from which it is
abstracted,
in order to recognise it, as the distorted language of the actual
world, and to realise that neither thoughts nor language in themselves form a
realm of their own, that they are only manifestations of actual life."
[Marx
and Engels (1970), p.118. Bold emphases
alone added.]

Indeed, Engels's approach
in this area began to falter
the moment he attempted to squeeze some metaphysical juice out of such desiccated
philosophical raisins; that is,
when he tried to extract 'paradoxical' conclusions from a few rather innocent-looking
words.

Naturally, only those who have already
accepted the view that reality is fundamentally 'contradictory' will agree with
the conclusions Engels drew. Others, however,
might be forgiven for remaining sceptical
-- particularly those who (not unreasonably) think that Engels's 'solution' is far more puzzling
than the original 'problem' had ever been.
Indeed, if the nature of motion is
problematic, calling it "contradictory", while making no attempt to explain how
that actually accounts for
anything, is worse than useless.

If these
'contradictions' do no work (again, as was argued
above), then their presence
here is, at best, unhelpful. That is because we can now see that they are the product of an over-active imagination,
compounded by a naive acceptance of the Idealist gobbledygook Hegel and Zeno
inflicted on
their readers.

In that
case, Engels's 'analysis' is an obstacle to our understanding, which
will, of course, need to be removed if science (let alone Marxism) is to advance.

In fact,
Engels failed to consider other, far more likely possibilities; indeed,
it looks like it never even occurred to him that his 'contradictory' conclusions
mightn't
follow if he had instead given consideration to the full range of words, or meanings,
available to ordinary language users. To be sure, these are easily
accessed by
those determined to use the vernacular with far greater concern for consistency, honesty and
sensitivity than Engels, Hegel, or Zeno ever managed.24

Engels clearly wanted to make a specific point about the paradoxical implications of a
handful of seemingly innocent (if not straight-forward) ordinary words. As we will see, he did this by unwittingly altering
their everyday use/meaning while imagining that the import of several
other ordinary terms associated with them remained unaffected.

In doing this he wasn't, of course, alone. Semantic sleight-of-hand has
been the sport of choice throughout the
history of Traditional Philosophy; and the practice continues to this day. Even careful
philosophers often fail to notice that their own work involves what can only be
called "piecemeal selectivity" over the use of certain words.
Indeed, they have invariably assumed it is possible to
tinker around with a handful of specially-chosen expressions while the meaning of any
other words
normally associated with them remain unaffected. Selectivity like this is, alas,
double-edged. In fact, these associated words -- whose meanings in this
case Engels also simply took
for granted -- prove to be equally (if not more) problematic than those he
finally latched onto.

As we are about to see, this unexpected turn of events will not
only undermine Engels's 'analysis' of motion, it will vitiate every single
classical account, too.

If, according to Hegel and Engels, an ordinary word like "motion" possess 'contradictory'
implications, then perhaps other terms these two
failed to consider might have analogously paradoxical connotations, especially given this
perverse way of viewing language. What about the word "place", for
instance? What if it turns out to be just as 'problematic'? In such
circumstances, could we continue to accept the validity of Engels's conclusions
about "motion" if the interplay between these two intimately connected words is
more complex than he imagined, and an alteration to one only succeeded in
altering the other?

More pointedly: What if certain
uses of the word "place" neutralise Engels's interpretation of the word "move"?

Clearly, Engels's argument relies on the meaning of "place" remaining fixed
while he tinkered around with "move". But, if "place" itself has no single
meaning, then any conclusions based on the
supposition that it hasjust onemeaning will automatically come under suspicion. Worse still,
any argument based on one aspect of the ordinary meaning of "place",
which undercuts the 'philosophical' sense of "motion", will be
thrown to
even greater doubt. That is because, if connotations of the latter are
compromised by the slippery nature of the former (or, indeed, vice versa), the meaning of
neither will emerge unscathed, in view of their intimate connection.

In fact, as we are about to see, this in-built linguistic
intricacy has the salutary
effect of deflating the philosophically grandiose conclusions Engels and
others thought they could derive from a handful of mundane words -- when, for
example, they employed a non-standard application
of "motion" alongside what they took to be a standarduse of "place", and vice versa.

Many of the ambiguities mentioned above (in relation to Engels's analysis of
"motion") actually depend on systematic vagueness in the meaning of the word
"place" and its cognates. Even when translated into the precise language of
coordinate algebra, or geometry, the meaning of this particular word doesn't become much clearer
(when used in such contexts).

Of course, this isn't to criticise the vernacular; imprecision is one of
its strengths. Nor is it to malign mathematics! However, when ordinary words are
imported into Philosophy, where it is almost invariably -- implicitly or
explicitly -- assumed they have a single unique
(or 'essential')
meaning, problems invariably arise, as Wittgenstein noted:

"I think that essentially we have only
one language, and that is our everyday language.... [O]ur everyday language is
the language, provided we rid it of the obscurities that lie hidden in it.

"Our language is completely in order, as long as we are clear about what it
symbolizes." [Waismann (1979), pp.45-46.]

"You ask why grammatical problems are so tough and seemingly ineradicable. --
Because they are connected with the oldest thought habits, i.e., with the oldest
images that are engraved into our language itself (Lichtenberg)....

"Language has the same traps ready for
everyone; the immense network of easily trodden false paths. And thus we see one
person after another walking down the same paths....

"One keeps hearing the remark that philosophy
really doesn't make any progress, that the same philosophical problems that
occupied the Greeks keep occupying us. But those who say that don't understand the
reason this must be so. The reason is that our language has remained constant
and keeps seducing us into asking the same questions. So long as there is a verb
'be' that seems to function like 'eat' and 'drink', so long as there are the adjectives
'identical', 'true', 'false', 'possible', so long as there is talk about a flow
of time and an expanse of space, etc., etc. humans will continue to bump up
against the same mysterious difficulties, and stare at something that no
explanation seems able to remove....

"I read '...philosophers are no nearer to the meaning of
'Reality' than Plato got...'. What a strange state of affairs. How strange in
that case that Plato could get that far in the first place! Or that after him we
were not able to get further. Was it because Plato was so
clever?" [Wittgenstein (2013), pp.311-12e. Italic emphases in the
original; quotation marks altered to conform with the conventions adopted at this
site.]

Indeed, as it turns out, there is no such thing as
the meaning of the word "place" -- or, for that matter, of "move".

This lack of clarity carries over into our use of technical terms
associated with either word; the application of coordinate systems, for example,
requires the use of rules, none of which is self-interpreting. [The point of
that comment will emerge presently.]

Nevertheless, it is relatively easy to show
-- by means of the sort of selective
linguistic 'adjustment' beloved of metaphysicians, but applied in areas or
contexts they generally fail to consider, or, rather, which they choose to ignore
--
that ordinary objects and people are quite capable of doing the
'metaphysicallyimpossible'. The flexibility built into everyday language actually 'enables'
the mundane to do the magical, and on an alarmingly regular basis. Such
everyday 'prodigies'
don't normally bother us -- well, not until some bright spark tries to do a little
'philosophising' with them.24a

If the
ordinary word "place" is now employed in one or more of its usual senses, it is
easy to show that much of what Engels had to say about motion becomes
either false or uninteresting. Otherwise, we should be forced to concede
that ordinary people and objects can behave in extraordinary -- if not
miraculous --
ways.

L41: The strikers refused to leave their place of
work and busied themselves building another barricade.

Assuming that the reference of "place" is
clear from the context (that it is, say, a factory), L41 depicts objects
moving while they remain in the same place -- contrary to what
Engels said (or implied) was possible. Indeed, if this sort of motion is
interpreted metaphysically, it would involve ordinary workers doing the
impossible -- moving while staying still!

Of course, an obvious objection to the above would be that L41 is a highly contentious example,
and not at all the sort of thing that Engels (or
other metaphysicians) had in mind by their use of the word "place".

But, Engels didn't
tell us what he meant by this term; he simply assumed we would 'understand' his
use of it. [That was the point of the preamble in the previous sub-sections.]
Here is what he did say:

"Motion in the most
general sense, conceived as the mode of existence, the inherent attribute, of
matter, comprehends all changes and processes occurring in the universe, from
mere change of place right up to thinking....

"All
motion is bound up with some change of place,
whether it be change of place of heavenly bodies, terrestrial masses, molecules,
atoms, or ether particles.
The higher the form of motion, the smaller this change of place.
It in no way exhausts the nature of the motion concerned, but it is inseparable
from the motion."
[Engels (1954), pp.69-70. Bold emphasis
added.]

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Engels (1976),
p.152.]

There
is nowhere in there that tells us what Engels meant by "place".

It
could be countered that it is perfectly clear what he meant by his use of this
word -- but as we are about to see, that isn't the case.

If, however, it is now claimed that he didn't mean by "place"
a sort of vague "general location" (like the factory used in the above example), then that would confirm the point being made in this part of the
Essay: Engels didn't say what he
meant by "place" since there was nothing hecould have said
that wouldn't also have ruined his entire argument. Tinker around with the
word "place" and the meaning of "motion" can't fail to be compromised (again, as
noted above). That can
be seen by considering the following highly informal 'argument':

L42: Nothing that moves
can stay in the same place.

L43: If anything stays in the same place, it
can't move. [L42 contraposed.]

L44: A factory is one place in which workers
work.

L45: Workers move about
in factories.

L46: Any worker who moves can't stay in the same place
(by L43).

L47: Hence, if workers move they can't do so in
factories (by L44 and L45).

L48: But, some workers remain in factories while
they work; hence, while there they can't move (by L43).

L49: Therefore, either workers work and do not work in factories
-- or
they move and they do not move.

As soon as one meaning of
"place" is
altered (as it was in L44), one connotation of "move" is automatically affected
(in L45 and L46), and vice versa (in both L47 and L48). In one sense of
"place", things can't move (in another sense of "move") while staying in one
place (in yet another sense of "place"). But, in still another sense of both they
can, and what is more, they typically do both. Failure to notice this produces 'contradictions'
to order, and everywhere (as in L49).

Even so, who believes that workers work and do not
work in factories? Or, that they move and do not move while staying in the same place?

Clearly, Engels's 'theory' of motion has to be able to take account of ordinary objects if it
is to apply to the real world and not just to abstractions, or to
physically meaningless mathematical 'points'. But, that is precisely what his
'theory' can't do, as we
are about to
see.

It could be
objected that it would be possible to understand what
Engels and Hegel were trying to say if "place" is defined precisely
without altering the meaning of "move", contrary to the points raised in the
last few sub-sections of this Essay. In that case, it could be argued that if "place"
is defined by the use of precise spatial coordinates (henceforth, SCs), Engels's
account of motion would become viable again.

Or, so some might like to think.

Of course, the problem here is that in the example
given
above (concerning those
contradictory mobile/stationary workers), if we try to define the meaning of the
word "place" a little more precisely, it will come to mean something like:

F1:Df. Place:
A finite three-dimensional region of space large enough to contain the
required object.

Well, plainly, in that sense things can and do move
about while they remain in the same region (i.e., "place") --
since, by default, any object occupies such a region as it moves -- that
is, it must always occupy a three-dimensional region of space large enough
to contain it as it moves; it certainly doesn't occupy a larger or a smaller space
(unless it expands or contracts)! Moreover, objects occupy finite
regions as they move in relation to each other (or they wouldn't be able to move).

Hence, if defined this way, moving objects always occupy the same space -- and,
of we are to believe Engels,
hence they don't move while they are doing so! That is, if they always stay in the same space, they
can't move -- if we insist on characterising "motion" the way Engels and Hegel
thought they could.

As we have just seen, objects always occupy the same space, even as they
move. So, they both move and don't move! Plainly we need to be even more precise,
here.

Of
the countless problematic options there are available to us the following seem
to be most relevant to the
points at issue:

(1) If an object always occupies the same space
(which fits it like a glove, as it moves), then it can't actually move!

(2) If an object occupies a larger space as it moves, it must expand.

(3) If an object moves about in the same region of
space (such as a factory), it still can't move!

(4) However, if an object
successively occupies spaces equal to its own volume as it moves, the
situation is even worse, as we will soon
see.

So, if the
'region' concerned (in which, or by means of which, or even through which) an
object is said to move is constrained too much, nothing would be able
to move
-- this is Option (1).
Put
each worker in a tightly-fitting steel box that exactly fits him or her and
watch all locomotion grind to a halt.

On the other hand, put that worker in a
larger region of space, and he/she
still won't be
able to move
-- this is Option (3). That is because if we define motion as successive occupancy of
regions of space within a broader region, then this worker can't move since he/she is always in the same
broader region, the same space -- for example, a factory.

The difficulty here is plainly one of
relaxing the definition of the required region that an object is allowed to occupy sufficiently enough to
enable it to move from
one place to another without stopping it moving altogether. Hence,
this problem revolves around preventing Option (3) from undermining what we might
ordinarily want to call motion -- the successive occupancy of certain regions of
space; i.e., the first half of (4) --, all the while
providing an account that accommodates the movement of medium-sized objects in
the real world.

But,
once this has been done (if we, say, relax the definition of the space, or the
place, concerned, making it larger, of
example) the above difficulties soon
re-appear; for it is quite clear that such objects will still move while staying in the
same place -- i.e., if the place allowed for this is big enough for them to do just
that!

Indeed, this fact probably accounts for, or
permits, most (if not all) of the
locomotion in the entire universe. Clearly, in the limit, if anything moves in nature it must remain in the
same
place, i.e., it must remain in the universe! Unless an object travels beyond the
confines of the universe, this must always be the case: the said object moves while remaining in the same
place -- i.e., it remains in the universe! Of course, this relaxes the definition
of "same place" far too much. But, the problem now is how we are to tighten the definition
of "place" so that objects aren't put in straight-jackets once more. [I.e., Option (1).]

At first sight, the above objection
(concerning a precise enough definition of "place") seems reasonable enough.
Engels clearly meant something a little more specific than a vague or general
sort of location (like a factory). But, if so, what? He didn't say, and his
epigones haven't, either. Indeed, it is quite clear that they
don't even recognise this as a problem, so sloppy has their thought become.
[And good luck finding a clear definition in Hegel!]

It might seem possible to rescue Engels's argument if tighter protocols for
"place" are prescribed --, perhaps those involving a reference to "a
(zero volume) mathematicalpoint, in three-dimensional space, located by the use of precise
SCs". But, this option would embroil Engels's account in far more intractable
problems. That is because such an account would (plainly!) relate to
mathematical point locations, or the movement of mathematical points
themselves -- and, as we saw earlier, that
is a non-starter.

[SC = Spatial Co-ordinate.]

Clearly, things can't
move about in such points -- but that has nothing to do with the supposed nature of reality.
Mathematical points can't contain anything. That is because mathematical points aren't containers. They have no volume and are made of nothing. If this weren't the case, they
wouldn't be mathematical points, they would be regions, or volume
intervals. [More on those presently.]

As noted above, if Engels meant something like this (by his use of "place"), his
account would fail to explain (or accommodate) the movement of gross material
bodies in nature, for the latter don't
occupy mathematical points.

And,
it is no use appealing to larger numbers, or sets, of such points located by SCs
(or by means of other technical devices);
no material body can occupy an arbitrary number of points, since points
aren't
containers.

Perhaps we could define a region (or a finite
volume
interval) by the use of SCs? Maybe so, but this would merely introduce another
classical conundrum (which is itself a variation on several of
Zeno's
other paradoxes): how it is possible for a region (or a volume interval) to be composed of
points that have no volume. Even an infinite number of zero volume
mathematical points adds up to zero. Now, there are those who think this
conundrum has a solution (just as there are those who think it doesn't), but it
would seem reasonably clear that the difficulties surrounding Engels's 'theory'
aren't likely to be helped by importing several more 'problems' from another set
of paradoxes -- especially when those paradoxes gain purchase from the
same linguistic ambiguities and vagaries about "space" that bedevilled "motion".

We seem to be going round in circles.

[No
irony or pun intended.]

Be this as it may, it is far more likely that Engels's use of the word "place"
is an
implicit reference to
a finitethree-dimensional volumeinterval (whose limits
can be defined by the application of well-understood rules in
Real
and
Complex Analysis,
Vector
Calculus, Coordinate Algebra and
Differential Geometry,
etc.).

Clearly, such volume intervals must be large enough to hold (even temporarily) a
given
material object. If so, this use of the phrase "volume interval" would in principle
be no different from the earlier use of "place" to depict the movement of those workers!
If
they can move about in
locations big enough to contain them, and who remain in the same place while
doing so, Engels's moving objects seem to be able to do likewise -- except they would now have a more precise "place"
or region
in which to do it.

However, and alas, this sense of "place" is no use at all, for
when such workers move, they will, by definition, stay in the same place! So, it
seems this must be the case with Engels's moving objects, if we were to depict "place" this
way.This
is just Option
(3), again!

(3) If an object moves about in the same region of
space (such as a factory), it still can't move!

Naturally, the only way to avoid this latest difficulty would be to argue that:

F2: The location
of any object must be a region of space (i.e., volume interval) equal
to that object's
own volume.

This is in effect
one
of the classical definitions. In that case, as the said object moves, its
own exact volume interval would move with it; the latter would follow each moving object around more
faithfully than its own shadow, and more doggedly than a world-champion bloodhound. But,
plainly, if that were the case, it would mean that any such object would still move while
staying in the same place -- since, plainly, any object always occupies a
space equal to its own volume, which would, on this view, travel everywhere with it, like a sort
of metaphysical glove.

This is Option (1),
again!

(1) If an object always occupies the same space
(which fits it like a glove, as it moves), then it can't actually move!

As should now seem plain: in this case we now have two problems where once
there was just one, for we should now have to explain
not only how bodies can move, but how it is also possible for volume intervals to move so that they can
faithfully shadow the objects
they contained!

Moreover, and far worse: in this instance, not only would we have to explain how locations
(i.e., volume intervals) are themselves capable of moving, we would also
have to explain what on earth they could possibly move into!

What
sort of
ghostly regions of space could we appeal to in order to allow regions of space
themselves to move into them?

Even worse still: these 'moving volume intervals'
must also occupy volumes equal to their own
volume, if they are to move (given this 'tighter' way of characterising
motion, expressed in F2). And, if they do
that, then these new 'extra' volume intervals (containing the original volume intervals
which also contain the moving body) must
now act
as secondary
'metaphysical containers', as it were, to the original 'ontological gloves' we
met earlier. Metaphorically speaking, this
theory, if it took such a turn, would be moving backwards, since an
infinite regress would soon confront us as spatial mittens inside containing
gloves, inside holding gauntlets, pile
up alarmingly to account for each successive spatial container, and how each of
them could
possibly move without another one to enable it to do just that!

F2:
The location
of any object must be a region of space (i.e., volume interval) equal
to that object's
own volume.

As seems reasonably clear, we would only
be able to account for locomotion this way if each moving object were situated
at the centre of some sort of 'metaphysical onion', each with a potentially infinite
number of 'skins'!

It could be countered that even though objects occupy spaces equal
to their own volumes, as they move (locomote) they then proceed to occupy successive
spaces of this sort (located in the surrounding region, for example), all of
which are of precisely the right volume to contain the moving object that now
occupies them, and which can be located or defined precisely. On this revised
scenario, moving objects would leave behind their old volume intervals (their
old containers), successively occupying new volume intervals along their
trajectories, as they barrel along.

This now brings us to a consideration of Option (2), and/or Option (4) -- now
modified to (4a) --, from earlier:

(2) If an object occupies a larger space as it moves, it must
expand.

(4a) An object
successively occupies spaces (or volume intervals) equal to its own volume as
it moves.

I will reject (2) as absurd. If anyone wants to defend it, they
are welcome to all the headaches it will bring in its train.

Consider, then, Option (4a): Even if (4a) were a correct interpretation of what Engels meant,
and it also proved to be a viable option
-- and, indeed, if sense could be made of these new, and accommodating
successive locations without re-duplicating
the very same problem noted in the previous section --, no DM-theorist could afford to
adopt it. That is because dialecticians claim that moving
bodies occupy at least two such "places" at the same time,
being in one
of them and not in it at the same moment. Clearly, if motion were defined in such
terms (that is, if it were characterised as involving objects successively occupying spaces
equal to their own volumes), then moving objects would occupy at least two of
these
volume intervals at once.

In that case, 'dialectical objects' would not so much move as stretch or
expand! [Modified Option (2)!]

To see this point more clearly (again, no pun intended!), it might be useful to examine the above
argument a little more
closely.

If the centre of mass (COM) of a 'dialectically moving' object, D, were located at, say,
(Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1), at the same time (to satisfy the requirement that moving bodies occupy at least two such "places" at the same time,
being in one of them and not in it), it would have to occupy a space larger than its own volume
while doing so.

Let us call
such a space, "S", and let the volume interval containing
(Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1) beδV1,leaving it open for the time being
whether S and δV1 are the
same or are different. Thus, if the COM of D is in two
such places (i.e., (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1))at once,
D would plainly be in S, and would occupy δV1.

But, once again, that would
mean that D would move while remaining in the same place -- i.e., it
would remain inside S, or inside δV1
(whichever is preferred), as its COM moved from
(Xk, Yk, Zk) to (Xk+1, Yk+1, Zk+1),
in the same instant. [Option (3), again!]

[Except, we can't speak of a 'dialectal object' moving from
one point to the next since that would imply it was in the first
before it was in the second, and that it was in the second after it
was in the first. As we have seen, if such an object isin both
places at the same time, there can be no "before" and no "after",
here.]

This is perhaps better then:D would move while remaining in the same place -- i.e., it
would remain inside S, or inside δV1
(whichever is preferred), as its COM is located at both
(Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1),
in the same instant. [Option (3), again!]

Now, the only way to avoid the conclusion that D moves
while occupying the same place, or space, S and/or δV1
--, and hence that it appears to stay still while it moves, just like the 'mobile/stationary' workers we encountered
earlier --
would be to argue that
such spaces remain where they are while Dmoves into successive, new
locations, or new spaces. This seems to be the import of
Option (4a):

(4a) An object
successively occupies spaces (or volume intervals) equal to its own volume as
it moves.

But, as D moves it still occupies
δV1,
only we would now have to argue that as it does so it also moves into a newδV
each time -- say, δV2
-- except that δV2 must
now contain (Xk+1, Yk+1, Zk+1) and (Xk+2, Yk+2, Zk+2)
-- otherwise it wouldn't be a new
containing volume interval that satisfied the requirement
that moving bodies occupy at least two such "places" at the same time,
being in one of them and not in it.

Plainly, all objects have to occupy some volume interval or other
at all times (or they would 'disappear'). However, in D's case it has to do this
while also occupying new volume intervals at the same time as it
locomotes -- otherwise, as we
saw, it would move while being in the same place, which would imply that it didn't move,
after all!

So, if D
occupies only one S, or only one
δV, at once, it would be at rest in either. [This is Option (1)
and/or Option (3).] Hence, it must occupy at least two
of these at the same time (if, that is, we accept the 'dialectical' view of motion).

That being so, the only apparent way of avoiding the conclusion that D-like
objects move while staying still is to argue that they occupy two successive
Ss, or two successive δVs (perhaps these partially 'overlap',
perhaps they don't), at once. Unfortunately, this would now mean that D-like
objects would have to occupy a volume, or a volume interval, bigger than either
one of S
or δV on their own, at once, and hence: they must expand or stretch.

It could be objected that two successive δVs would
contain
(Xk, Yk, Zk)
and
(Xk+1, Yk+1, Zk+1)
each between them
--
that is, δV1
would contain
(Xk, Yk, Zk) and δV2
would contain (Xk+1, Yk+1, Zk+1)
--, so the above objection is misguided. Maybe so, but the point is that dialectical
objects must occupy two δVs
at once, and if that is so, both δVs must
contain
(Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1),
jointly or severally, otherwise such moving objects couldn't occupy two spaces (two
δVs) at
the same time.

Now, if that
were so, and D wasn't stationary while it occupied δV2, as we saw
above in an analogous context, it must also occupy δV3at the same time, otherwise it will be stationary while in δV2, and so on.
Successive applications of this
argument would have D occupying bigger and bigger volume intervals (i.e.,
δV1 + δV2 + δV3+ δV4 +...,+
δVn),
all at the same time. In
the limit, D could fill the entire universe (or, at least, the entire
volume interval encompassing its own trajectory), all at the same time -- if it moves, and
if Hegel is to be believed!

There thus seems to be no way to depict the
motion of D-like objects that
prevents them from either (i) moving while staying still, or, (ii) expanding alarmingly like some sort of metaphysical
Puffer Fish.24b

The reader should now be able to see for
herself what mindless mystical mayhem is introduced into our reasoning by this cavalier
use of (contradictory) metaphysical language. When one sense of "move" is
altered, one sense of "place" can't remain the same, nor vice versa.

Of course, no one believes the above
ridiculous conclusions, but there appears to be no way to avoid them using the
radically defective and hopelessly meagre conceptual and/or logical resources DL supplies its
unfortunate victims -- compounded by their cavalier use of ordinary language.

Dialectical headaches don't stop there,
either. It seems that 'Dialectical objects' must
also
concertina as they move.

Consider a simple body, B, made of 3 connected parts: P1,
P2 and P3,
all arranged in the same line, so that there are no gaps between them.
Let B move such that at t1,
the centre of the leading edge of P1
is at (X1, Y1, Z1),
the centre of the leading edge ofP2
is at (X2, Y2, Z2),
and centre of the leading edge of P3
is at (X3, Y3, Z3).
Let us also assume that the centre of the leading edge of P3
now moves to (X4, Y4, Z4).
Finally, let us assume that the distances between each of (X1, Y1, Z1),
(X2, Y2, Z2), (X3, Y3, Z3)
and (X4, Y4, Z4)
are all the same.

Now, if all moving objects occupy two places at once, and if B
moves in a line parallel to the line joining the centre of the leading edge of
P1 to the
centre of the leading edge of P3,
then the centre of the leading edge of P1
must occupy (X1, Y1, Z1)and (X2, Y2, Z2),
the centre of the leading edge of P2
must occupy (X2, Y2, Z2)and (X3, Y3, Z3),
and the centre of the leading edge of P3
must occupy (X3, Y3, Z3)and (X4, Y4, Z4),
at the same time. In effect, B would concertina as it moved, with the
front end of, say, P1
crushing or penetrating the back end of P2,
and overlapping it right up to its own leading edge -- in effect, wiping P2
out!

[Again,
this result depends on the answer to an
earlier question: How far apart are
the two places a moving body occupies that Engels envisaged? If this is left indeterminate, then any
length will do. Even then, if a specific length is decided upon, we could make
the distance between the above parts equal to that length, and the same
result would still
follow. (That has been done below, anyway.)]

It can't be the case that the trailing edge of
P2
will leave (X2, Y2, Z2)
just before the leading edge of P1
reaches it, since, as
we have already seen, there is no before and now after here, since all
such motion must take place at the same time for it to constitute a 'dialectical
contradiction'.

Now, it could be objected that P1
and P2, for
example, will occupy the space between (X1, Y1, Z1)
and (X2, Y2, Z2)
and (X2, Y2, Z2)
and (X3, Y3, Z3), respectively, as B moves
-- but this isn't possible. That is
because there are no gaps between any of the three parts of this object for any
of those parts to move into. So, if B were, say, a single carriage train,
then P1
would comprise the rear section of that carriage, P2
the middle third, and P3
the front end. This view of motion would therefore have those parts of this
single carriage crushing the one in front.

[I have considered the
option that there is just such a gap, again, below.]

It might be argued that the structural properties of B
(i.e., intermolecular forces, etc.) will prevent this from happening. That is
undeniable, but this response also has the unfortunate consequence that while B
may be in two places at once as it moves, none of its parts could be! And
that in turn would imply that while B was racing along, none of its
parts would be racing along with it -- since they are not allowed by these 'structural
properties' to be in two places at once!

Similar, if not worse problems afflict any 'dialectical objects'
undergoing circular or more complex forms of movement, such as helical or spiral motion.

So, consider a rotating disc, D, of negligible thickness
divided by a diameter line, T, into two equal semi-circular sectors, S1
and S2. If
we define the centre of this disc as the origin, then we can set the leading edge of S1
so that it
lies along T. In addition, let there
be a point, p1,
on T, r units from the centre, with co-ordinates (r, θ1).
Let the leading edge of S2
also
lie along T, and let there
be a point, p2,
r units from the centre, with co-ordinates (r, θ2).
Plainly, this means that p1
and p2
lie on the same trajectory, a circular locus r units from D. [I have used
polar co-ordinates in two-dimensions here to simplify this
example.]

Now, if all moving objects occupy two places at once, and if B
rotates clockwise, then the leading edge of S1
must pass through both p1andp2,
and the leading edge of S2
must pass through both p2andp1,
at the same time. But this is even worse than the 'dialectically linear
movement' considered above, since, in this case, either (i) D will
totally disappear -- as both of its sectors occupy the same semi-circle that the
other one occupied -- or, (ii) Both of these sectors must stretch to cover the
entire disc, ramming into the back of one another as they did so, compressing
each into a region with zero area!

Now it might be possible to defend this picture of dialectal
objects as they smash into one another by arguing that the above scenarios have
been deliberately biased against DM. For example, in the linear case above, while the centre of the
leading edge of P3
might move to (X4, Y4, Z4),
the distance between (X3, Y3, Z3)
and (X4, Y4, Z4)
need not be equal to that between (X1, Y1, Z1)
and (X2, Y2, Z2),
or that between (X2, Y2, Z2)
and (X3, Y3, Z3).
Let us say, therefore, that the distance between (X3, Y3, Z3)
and (X4, Y4, Z4) isδL.
In this case, therefore, B will move forward δL units, as
will each of its parts.

This would have the effect on S1
such that it would no longer move to (X2, Y2, Z2),
but to some intermediate point (X1+δx, Y1+δy, Z1+δz),
with the same sort of thing happening to the other leading edges. The same would
also happen to the trailing edge of S2,
which, let us say was at (Xi, Yi, Zi),
at t1. Now, the trailing edge of S2
and the leading edge of S1
can't occupy the same space, as should seem obvious;so let us say that
the distance between (X1, Y1, Z1) and (Xi, Yi, Zi) can be made as small as we like -- let us stipulate that this is
δU(where it
is left open whether or not δU
>δL).
In that case, there would be a gap, δU,
between at least two of the parts.

Hence, the trailing edge of S2
would move to (Xi+δx, Yi+δy, Zi+δz)
while the leading edge of S1moves to (X1+δx, Y1+δy, Z1+δz).
Plainly, these are not the same points. [Anyone who disagrees should read the
subscripts more carefully!] If so, S1won't smash into the back of S2
as imagined above. The same sort of conclusion can be drawn in connection with
the rotating disc.

Unfortunately, this reply fails, too. That is because the centre
of the leading edge of S1
has to occupy two places at once, if Engels and Hegel are to be believed.
So, the centre of the leading edge of S1
has to occupy (X1, Y1, Z1)and(X1+δx, Y1+δy, Z1+δz),
and the centre of the trailing edge of S2
has to occupy (Xi, Yi, Zi)and(Xi+δx, Yi+δy, Zi+δz),
at the same time. Now, if δU
is zero, then (X1+δx, Y1+δy, Z1+δz)
will lie beyond (Xi, Yi, Zi),
which means that the leading edge of S1will smash into the back of S2.
The same will happen if δU
<δL. On the other hand, if
δU
>δL, a gap will open up between S1
and S2,
which will widen all the more as B continues to move. So,
B will either (a) Begin to fragment, or (b) Concertina, as
it moves. The same will happen to the disc.24b1

Despite this,
it could be argued that if the ordinary word "place" is really quite so vague then it should
be replaced with more precise concepts; those defined in terms of SCs,
once more. But, as the following argument shows, that would be another backward
move (no pun intended!):

L52: However, when written correctly, the elements in such
3-tuples
must occupy their assigned places (by the ordering rules). Consider then the
following ordered triplet: <x1, y1,
z1>.
Each element in this SC must be written precisely, with xi, yi, and zi
in their correct places.

L53: But, the situating of such elements can't itself be
defined by exact SCs, otherwise an infinite regress will ensue.

L54: Consequently, the latter sense of "place"
(i.e., that which underlies the ordering rules for SCs) can't be defined (without circularity)
by means of SCs.

[SC = Spatial Coordinate.]

This means that the definition of "place" by means of SCs is itself
dependent on a perfectly ordinary meaning of "place", and, further,
that the latter sense of "place" must already be understood if a co-ordinate system is
to be set-up correctly.

Therefore, the ordinary word "place" can't be defined without circularity by means of a coordinate
system!

In short, the precision introduced by means of SCs is bought at the expense of
presupposing mundane linguistic facts such as these.

Of course, this isn't to malign or depreciate coordinate geometry, it merely
serves to
remind us that any branch of human knowledge (even one as technical and
precise as modern
mathematics) has to mesh with ordinary language and everyday practice (at
some point), if it is to be set-up to begin with, and if human beings (or
machines programmed by human beings) are capable of using it. Everyday facts like these are
soon forgotten (in the course of one's education), since, as Wittgenstein
pointed out, we are taught to quash or dismiss such simple questions early
on. As a result we inherit the mythological structures that previous generations
have built on top of unexamined foundations like this.

We
might even adapt a famous passage from Marx's Eighteenth Brumaire to
illustrate this point (no pun intended):

"Mathematicians construct their coordinate systems, but they do not do so as
they please; they do not make them under circumstances of their own choosing,
but under circumstances already existing, given and transmitted from the past.
The tradition of all dead generations weighs like a nightmare on the brains of
the living." [Edited
misquotation
from
Marx (1968), p.96.]

If, on the other hand, a typographically
identical word (viz.: "place") were to be defined in the above way, and then
used in mathematics or physics, it wouldn't be the same word as the ordinary
word "place" upon which the definition itself had been
predicated. And, if this new term, "place", is used to define the movement of objects in
DM, then the motion of gross bodies in the material world would still be unaccounted for.

It
could be objected here that it is surely possible to disambiguate the
ordinary word so that it could be employed in a
DM-analysis of motion --, meaning that it was no longer confused with the less precise phrase,
"general location".

Since this has yet to be done (even by DM-advocates, who, up
to now, have shown that they
aren't even aware of
such problems, and are highly likely to ignore them once they have been apprised of
them, categorising such concerns as "pedantic"!) it remains to be seen whether this promissory note is
redeemable. However, even if it were, it would still be of little
help. As we have seen, and will see again, the word "place" (even as
it is used in mathematics) is
itself ambiguous, and necessarily so. [There is more on this in Note 25.]

Moreover, Engels's account requires motion to be depicted by a
continuous variable, while one or both of time or place is/are held to be
discrete, otherwise a contradiction wouldn't ensue (which is, of course,
something even Hegel recognised).24d This
con-trick is accomplished
either by (i) The simple expedient of ignoring examples of
discrete forms ofmotion (several of which are given below),
or (ii) Failing to consider
instances where both time and place are continuous -- all the while
(iii) Imagining that the relevant words drawn from ordinary language used to depict both have been employed
in their usual senses, and haven't been altered by forcing them into these novel contexts.25

Even assuming a stricter
sense of "place" could be cobbled-together, somehow, it would still
be of little help. That is because it would either make motion itself impossible --
or, if possible, incomprehensible -- since, given Engels's account, a moving
object would have to be everywhere along its trajectory, if it is
anywhere -- and, it wouldn't
so much move as expand, stretch, concertina, or vanish, as noted above.

If the points made above are valid (again, no pun
intended), it means that in a
perfectly ordinary sense, bodies can both move and stay in the same place
while doing so. Indeed, they are quite capable of remaining stationary
even if they undergo a change of place, moving and not moving all at once!

The first of these possibilities was depicted above with respect to those
stationary/mobile workers; the second
(where something can both move and not move all at once -- and, in
this case, that would involve a discrete sense of "move", into the bargain), is illustrated
by the next
example:

L55: NN was second in line when
MM, who had been first in the queue, suddenly dropped out. Hence, NN
moved to the front of the queue even though he remained rooted to the spot.26

In L55, we have a perfectly ordinary example where a fellow human being manages to do the
'metaphysically impossible' (without even breaking into a dialectical sweat), moving while staying
still (relative to some inertial frame). Clearly, it is possible to move to
the front of a queue (in one sense of "move") even without moving at all (in another sense
of "move"), relative to some inertial frame. This example even satisfies
Engels's caveat that movement is connected with "change of place".

Indeed, it
is
also possible to think of cases of discontinuous (i.e., discrete) motion whereby, even
though something once moved, nothing need now be moving -- and yet in one
sense something still moves. This would also involve whatever it was that
managed to do this 'moving and not moving at the same time', doing so in a different
sense from that which was illustrated in L55. In fact, it is possible to show that some things
can move (again in a discrete sense) while they occupy none of the
intervening places between successive locations. All of these
at first sight, rather odd possibilities are illustrated below:

L56: The footprints moved across the snow-covered yard,
indicating where the scabs were hiding.

L57: Easter moves to a new date each year.

L58: "See, the page numbers at the
top of the page in this book you sold
me move about erratically. It has been printed and bound all
wrong!"

L59: The ground staff moved the cricket pitch to the other side
of the square.

L60: The organisers of the rally moved the meeting to seven
o'clock.

L61: The strobe light moved across the floor picking out each
dancer, one at a time.

In L56, we have stationary 'objects' (i.e., the footprints created by
individuals who had earlier walked across the said yard), which still move (across
the yard) even while each item (each footprint) is stationary.

In
L57, nothing actually moves even while it still does! In L58, nothing moves,
once again, but yet something actually moves (namely the faulty numbering), and
it does so discretely while not occupying any of the intervening spaces, which
spaces don't exist either for anything to move into! [Of course, in such
circumstances, we would
probably use "jump" instead of "move". But, to jump is also to move.]

A similar picture emerges in L59,
where a discrete object (a cricket pitch) is moved a certain distance (between,
say, twenty and thirty metres -- sixty to ninety feet), but which object (this
cricket pitch)
doesn't existwhile it is moved, nor does it occupy any of the intervening spaces
on its 'journey', but which intervening spaces do exist! Similar
situations are illustrated by L60 and L61.

Not only that, but continuous, and yet stationary,
objects can move while remaining still:

L62: As I look down on the scene, an immobile line of
pickets moves out of sight, curling right round the block; each worker holding
her ground, rooted to the spot.

L63: The wire moves in a
spiral around this tree. It has been in the same spot so long that the tree has partially grown around it.27

Finally, some things can move -- but to
nowhere in particular -- and they can stay quite still while they are doing it:

Such mundane examples (there are countless others), using
perfectly ordinary words in situations we
all readily recognise and comprehend, demonstrate that the seemingly 'obvious'
metaphysical principles that thinkers like Engels dreamt-up actually depend on
non-standard applications (i.e., distortions) of the vernacular (indeed,
as
Marx pointed out).

So, what at first sight might seem distinctly odd now turns out to be
nothing more than a rather prosaic set of examples with which we are all familiar, and which
would hardly raise an eyebrow in everyday life.

Of course, it could be objected that these examples of 'motion'
aren't what Engels meant by "motion"; indeed, he was quite careful to
emphasise that he was only interested in one sort of motion: continuous change of
place with respect to time:

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical
change of place can only come about through a body being both in one place and
in another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous
solution of this contradiction is precisely what motion is." [Engels (1976),
p.152. Italic emphasis added.]

"All motion is bound up with some
change of place, whether it be change of place of heavenly bodies,
terrestrial masses, molecules, atoms, or ether particles. The higher the form of
motion, the smaller this change of place. It in no way exhausts the nature of
the motion concerned, but it is inseparable from the motion. It, therefore, has
to be investigated before anything else." [Engels
(1954), p.70. Italic emphasis added.]

"Among natural scientists motion is always as a matter of
course taken to mean mechanical motion, change of place. This has been handed
down from the pre-chemical eighteenth century and makes a clear conception of
the processes much more difficult. Motion, as applied to matter, is change
in general." [Ibid.,
p.247. Italic emphasis in the original.]

In the above, Engels was perfectly clear that he meant "simple mechanical
change of place", which is radically different from the non-standard uses of the word
illustrated above.

Or, so it could be
argued.

[Of course, this doesn't mean that Engels
didn't recognise other, more complex forms of motion; quite the opposite, in
fact!]

Unfortunately, however, as we have seen, it isn't easy to ascertain what (if anything) Engels actually
had in
mind by "simple mechanical change of place". Indeed, much of what
he said is compatible with no movement having occurred, so that the supposedly
'contradictory' aspects of an object's trajectory have
nothing to do with whether that object was or wasn't moving.
Moreover, as we have also seen, Engels's use of language implies that 'dialectical' objects threaten
to expand
alarmingly, concertina destructively,
or spread out and occupy an
entire region, whenever they try to move.

Furthermore, dialecticians can't appeal to what we 'all know' about the meaning
of the word "motion", nor should they suppose we 'all know perfectly well' what
Engels meant when he spoke about it. As the above examples indicate, there is no one thing we all mean by this
word (and its associated terms), even though most (if not all) speakers know
what they mean
when they are used in ordinary contexts
(like those depicted above). Indeed, we have just seen that objects can move
even while they don't undergo a "change of place", contradicting Engels
-- and, they can undergo a "change of place" and remain perfectly still
while they do it.

And, as far as
Engels's own use is concerned, we may only agree with the claim that
DM-theorists know what Engels meant by "motion" when they succeed in
explaining to the rest of us, with some clarity, precisely what that is!

Unfortunately, to date, there have been no significant moves in
that direction (irony intended).

In addition, the above examples were deliberately
taken from everyday situations
-- those that are readily understood. It is Engels's (Hegelian) use of the word
"move" that turns out to be non-standard and, in the end, incomprehensible.

Finally, it
might be felt that the above emphasis on the ordinary sense of words is
inappropriate in a scientific or philosophical analysis of motion and change.
This objection was
considered in detail elsewhere
at this site. Anyway, Engels himself
used what look like ordinary words to make his point -- which was that every example
of motion in the universe involves a contradiction, including those parts that can be depicted by
a use of the vernacular.29

Again, it could be argued that any account of motion has to involve contradictions
because of what must be the case if objects in reality -- independent
of thought -- actually move, which they clearly do. Hence, despite what
we might say, the real world exhibits countless examples of
motion and change, each of which is contradictory.

However, this
use of modal
terms is quite revealing for it confirms something that has
been implicit all along (and hinted at earlier): this traditional 'family of arguments' depends on
inferences from the alleged meaning of a few specially-selected words
-– albeit given an idiosyncratic re-interpretation, often in isolation from other associated
terms, and divorced from their ordinary contexts of use -- to 'necessary truths'
about fundamental features of the world.
'Deductions' like these invariably precede even a perfunctory empirical 'investigation' -- if, that is, the latter is so much as
attempted by dialecticians. The results these inferences appear to warrant
are then regarded as absolute certainties, which their inventors find
impossible to question. That is, of course, because these
Super-truths are based on language alone, not on evidence. [On this in general, see Essay Twelve
Part One.]

As pointed out earlier, Engels performed no controlled experiments
(or any at all) or detailed observations, before or after he drew
his hyper-bold conclusions about motion. In fact, it is impossible even to describe
a single observation or experiment -- other than a thought experiment,
which would, anyway, depend on the sorts of ambiguities highlighted above -- that
could conceivably confirm Engels's claims about motion. This is partly
because 'contradictions' themselves can't be observed (although an inscription
of a proposition and its contradictory can, of course, be observed -- on that,
see here),
and partly because of the modal, universal and omni-temporal character of the
conclusions themselves.30

This means that the only substantiation Engels could have
offered to support his claims would have been
language-based; he would have had to have referred
anyone sceptical of his conclusions to what certain words really meant.
It would be no good advising non-believers to look harder at the phenomena,
refine their search or redo their experiments --, which is, of course, why one finds
no
evidence at all in books on dialectics aimed confirming or even so much as vaguely supporting
the theory that motion is contradictory. What we find in its place is a set
of dogmatic assertions, which are themselves (often) linked to a very brief thought experiment
-- both
of which are based on a brief consideration of a handful of the words or concepts involved.

[Readers are invited to check!
E-mail me if they know of, or have found
any such evidence, or they manage to locate a DM-supporter who references any.]

Furthermore, this is a doctrine that can't even be confirmed in practice!
One would have thought that that fact alone would have rung alarm bells in a few
dialectical heads!

Thus, Engels's only 'evidence' was based on
a
philosophical use of language -- in fact, on Hegel and Zeno's use of it --,
but not on how such words feature in everyday
life. This
predicament (which he shares with all other metaphysicians) invariably
passes unnoticed because (i) This is almost universal in Traditional Philosophy, (ii) It has been going on now for well over
two thousand years ('East' and 'West'), and (iii) It is thought that by
looking at certain words (or their 'real' meanings) the Armchair
Philosopher is actually examining the world itself, and not simply the
supposed meaning of a few
specially-selected, jargonised expressions, which, because of this, have been divorced from
reality.

The Idealist implications of the traditional approach to
'knowledge' were
once again well summarised by George Novack:

"A consistent materialism cannot proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphasis added.]

[The reason for this age-old confusion of talk about talk with
talk about things is examined in detail in Essay Twelve
Part One (as well as throughout
the rest of Essay
Twelve -- summary
here).]

Nevertheless, the
denotation
of the specialised jargon concocted by Traditional
Theorists is
simply taken for granted; indeed, the question whether such words actuallyhave a denotation is seldom even raised.

The unremittingly negative view of philosophical word-magic presented
at this site gains
support from the additional fact that 'philosophical problems' like this can't be solved by an appeal to evidence. That is why they depend
solely on a
distorted use of language,
and it is also why this
is all Engels ever offered his readers (in this area), and why it is all he could
ever have offered
his readers.

Nevertheless, Engels
restricted his comments neither to examples of motion he had personally
investigated, nor to the entire set of examples experienced by humanity
up until his day.
Despite this, he still felt confident that he could extrapolate from his own understanding of a
few ordinary-looking words to conclusions that were applicable to every conceivableinstance of motion anywhere in the universe, for all of time:

"Never anywhere has there been matter
without motion, nor can there be…. Matter without motion is just as
inconceivable as motion without matter. Motion is therefore as uncreatable
and indestructible as matter itself…." [Engels (1976), p.74. Bold emphases
added.]

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Ibid., p.152.
Bold emphasis added.]

In fact, what Engels actually did -- and this was the extent of the 'careful' scientific
research he carried out in this area -- was toreproduce the analysis of
motion he found in Hegel's Logic!

And, truth be told, Hegel hasn't gone down in history as a great experimental
scientist, either.

As we shall see (in Essays Nine Part
One and
Two, and Twelve (summary
here)),
these all too easily overlooked facts possess several revealing ideological implications of their
own.

Engels's
feeling of confidence in the conclusions he so effortlessly drew no doubt arose from his
consideration of one particular interpretation of "motion" (but no others).
Hence, we find him claiming that:

"[E]ven simple mechanical change of place can only
come about through a body being both in one place and in another place at one
and the same moment of time, being in one and the same place and also not in
it." [Engels (1976),
p.152.]

But, how could Engels possibly
have known
this? How could he have been so sure that every single instance of motion
throughout the
entire universe, for all of time, could only proceed in the
way he alleged? If we rule out the absurd idea that Engels was a
deity of some sort, there are in fact only two possible answers to that
question:

(1) His certitude was based on his grasp of the 'concept'
of motion itself. But, as seems obvious from his comments,
Engels actually based his conclusions on his own understanding of a strictly
limited set of words
about motion -- on the ideas he lifted from Hegel -- but not on the 'concept' of motion itself (if there is
such a thing). Neither he nor anyone else has access to such a concept
independently of the words which supposedly allude to, or which express, it.

And yet, divorced from the wide variety of ways we ordinarily
talk about motion (illustrated by the many examples given in this Essay), who is
to say what is the correct way to understand such words in novel contexts
like this?
Or, whether the meaning of any technical terms that have been co-opted and
pressed into service are the same as
the meaning of the ordinary words
they supposedly replaced or superseded? Or, that there is only one way to interpret them?
Or, that Engels and Lenin hit upon the correct way to comprehend them
(and then only after reading Hegel -- as opposed to sifting through the
relevant scientific or observational data)? Or even, whetherthelanguage they finally employed means anything at all?

However, and more to the point: precisely who decided
that such off-the-cuff conclusions (about substantive features
of the world, true for all of space and time) can be read off from the alleged meaning of a few words?

Did the rest of us miss a meeting?

(2) The second possible answer revolves around a likely response that might have
occurred to several readers: Surely a rejection of Engels's understanding of
motion would be paradoxical, if not contradictory. That is because
it would
represent a repudiation of what the concept of motionitself actually implies. Consequently, on
this view, anyone who fails to interpret motion along these lines (involving a body being
in two places at once (etc., etc.)) only succeeds in revealing that they have misunderstood what
motion is in-itself. Indeed, it would flatly contradict what we all
ordinarily understand motion to be.

Or, so it could be claimed.

However, Engels's analysis of motion is
paradoxical, if not openly contradictory, too; so even by its own lights there
appear to be equally good reasons to reject his interpretation of motion as
there are for accepting it, based on paradox alone. If it is paradoxical to reject his version, it is equally
paradoxical to accept it.

Moreover, an appeal to experience to decide between these two
alternatives is of little help, and for that is so for at least four reasons:

(i) As has already been pointed out, Engels drew his conclusions
about motion without
referring to any evidence at all. His views were clearly not based on
experience; in fact, they were aimed at interpreting reality beyond any and all
conceivable evidence and experience.

(ii) Our experience of motion is as ambiguous as the words we use
to depict it. The examples given above (and in the Notes below) indicate
that our ordinary ways of speaking about motion are far more complex than
Engels, Zeno, Hegel, or even Lenin imagined. [Of course, in their everyday speech they will have
shown that they already knew this; it was only when they began to 'philosophise' that
they allowed themselves to be led astray.] Anyway, not even an indefinitely large finite number of
observations of cats moving on and then off assorted mats (and the like), could
confirm whether motion is or isn't (a) continuous,
(b) discontinuous, or if it (c) is composed of countless discrete, concatenated 'sub-movements' -- or, indeed, whether
(d) it
is
something else for which we have as yet no words. Even with advanced technological assistance, we
still wouldn't be
able to tell if motion is the one or the other.

[Indeed, as we have seen, there is no one thing that
is
motion. Our use of this word, and its associated terms, is far too complex to
be constrained in this way. (See the next two points.)]

(iii) Ordinary language, and thus everyday experience -- as a
matter of fact -- allows for both sorts of motion:
discreteand
continuous. This was demonstrated in the above examples. It is only a metaphysical
prejudice (itself based on other priorities that will be exposed in Essay
Twelve (summary here)) that (a)
Consigns certain depictions of motion to the realm of "appearance", or
"commonsense", while others are supposed to refer to "reality itself";
or that (b)
Regards one type of motion as
primary, the rest secondary.

(iv) The notion that
there are such entities as "things-in-themselves" (or that there is something
called "motion-in-itself", or "motion itself") is hopelessly confused, and that isn't just because
this idea expresses a thinly disguised form
of "absolute" motion -- as will be argued elsewhere at this site
(until then, see Note 10). As we
will see, reference to "motion-in-itself" is unintelligible; small wonder then that it has
yet to be explained by anyone.31

Nevertheless, and once more, a repeated use of the word "must" in response to
the above -- as, for example, in a retort that might well have occurred to
some readers: "That's all very well,
but motion must involve a body being in two places at once…(etc., etc.)" --
could itself only have been based on aconceptual or linguistic analysis of a
limited range of words associated with movement, and their varied uses. Again, that would
amply confirm the view maintained in these Essays that dialecticians are happy to draw
universally true inferences from
a handful of specially-selected words,
and then foist the results on reality -- the use of "must" revealing yet again
this propensity to impose favoured a priori theses on nature.

When pressed to
provide evidence to substantiate their claim to be in possession of
Super-scientific knowledge of motion --
applicable to every region of space and time -- all that
DM-theorists would be able to offer in support is the supposed meaning of a few words!

Once again, apart from an absurd alternative explanation for their possession of superior
knowledge (i.e., that those making such claims are
deities of some sort who have access to a profound, semi-mystical
fountainhead
of knowledge (concerning
the nature of
"reality-in-itself")), 'conceptual or linguistic analysis' is the only conceivable source of
hyper-bold 'dialectical' claims like these.

And that explains why Engels omitted the data supporting his 'theory' -- and no one
since has bothered to supply any.32

It might be felt that the
above discussion completely misses the point: DM deals with real material
contradictions in the actual world, verified by careful empirical
investigation and tested in practice. Not only that, it is based on the thesis that reality
is contradictory (and that is itself founded on the scientifically confirmed belief in universal change).
It goes way beyond the idea that this is only true of the
language we use to depict nature. If contradictions in
nature are difficult to capture in ordinary language that is because ordinary
language is inadequate to the task (as, indeed,
TAR itself maintains;
cf., Rees (1998), pp.45-52). It certainly doesn't show that reality is free from contradictions.

However, this response won't do. Admittedly, the world is the way it
is independent of language and human knowledge, but unless we are capable of
expressing ideas about the world in a clear and determinate manner we are surely
in no position to make any definite claims about it. This is all the more so
with respect to DM where every attempt to render it perspicuous has failed -- as we
have just seen in relation to Engels's account of motion (and as we will see
with respect to other core DM-theses in other Essays posted at this site). This
is quite apart from the fact that it is impossible to verify Engels's claims
about motion "by careful empirical investigation and tested in practice", just
as it ignores the fact that practice is an
unreliable guide when it comes
to testing the truth of a theory.

Moreover, Engels certainly thought he could derive what he took to be a contradiction from
a consideration of ordinary words depicting movement and change. But, if his
'derivation' (and, indeed, Hegel's) is shot-through with vagueness and ambiguity, the
motivation to claim that reality is contradictory is fatally compromised; and it
fades further into oblivion when it is recalled
that this idea itself is based on a series of
egregious logical blunders that
Hegel committed. What is more, it will remain
in that state unless and until
DM-theorists produce the evidence that motion everywhere in existence (past,
present and future) is as they say it is -- or until they succeed in
demonstrating that they have an alternative way of 'intuiting' the 'deeper aspects
of reality'
that are mysteriously unavailable to the rest of us.

Objects and events in nature do not confront humanity already
sorted, labelled and categorised. We do not literally see contradictions in
reality; they require considerable argumentative stage-setting even before
dialecticians can themselves assert that they exist. Hence, the question whether
there are 'objective' contradictions in nature -- based as it is (in this case at
least) on a quirky misuse of language (almost on a par with the bogus question
whether the King in chess really did marry the Queen -- or, indeed, whether they
received planning permission to build those two Castles in the corner) -- is itself irredeemably
confused. And, of course, to such non-questions there are no answers.34

Plainly, it is the non-standard
interpretation that dialecticians put on ordinary words that conjures into
existence the
paradoxes they then label "contradictions" -- that is, even when
they manage to get that word right.

In which case, far from reality being 'contradictory', it is the
DM-use of language
that is incoherent and paradoxical.

In this Essay, we have seen that Engels's account of motion is
not only shot-through with ambiguity and equivocation, it is irredeemably
obscure.
Even if we knew what he was banging on about, his 'analysis' depends on
an asymmetric convention that places no limit on the divisibility of space
while it places a
limit on the divisibility of time.

Finally, we have also seen that his conclusions (even if we
knew what they were) only seem to follow if we ignore the many changes in
meaning that words like "place" and "move" undergo in different
contexts. In
fact, as things turned out, no sense at all could be made of what Engels was trying
to tell his readers.

But, what of the so-called 'Law of Identity'? Doesn't
it imply
that change and movement are impossible?

It is
impossible to form a clear idea of the DM-thesis that
reality is fundamentallycontradictory:

"Instead of speaking by the
maxim of Excluded Middle (which is the maxim of abstract understanding) we
should rather say: Everything is opposite.Neither in heaven nor in
Earth, neither in the world of mind nor of nature, is there anywhere such an
abstract 'either-or' as the understanding maintains. Whatever exists is
concrete, with difference and opposition in itself. The finitude of things will
then lie in the want of correspondence between their immediate being, and what
they essentially are.

"Contradiction is the very moving principle of the
world: and it is ridiculous to say that contradiction is unthinkable. The
only thing correct in that statement is that contradiction is not the end of the
matter, but cancels itself. But contradiction, when cancelled, does not leave
abstract identity; for that is itself only one side of the contrariety. The
proximate result of opposition (when realised as contradiction) is the Ground,
which contains identity as well as difference superseded and deposited to
elements in the completer notion." [Hegel
(1975), p.174;
Essence as Ground of Existence, §119.
Bold emphases added.]

"[B]ut contradiction is the
root of all movement and vitality; it is only in so far as something has a
contradiction within it that it moves, has an urge and activity." [Hegel (1999),
p.439,
§ 956. Bold emphasis added.]

"Dialectics…prevails throughout nature….
[T]he motion through opposites which asserts itself everywhere in nature,
and which by the continual conflict of the opposites…determines the life of
nature." [Engels (1954),
p.211.]

"[Among the elements of dialectics are the
following:] [I]nternally contradictory tendencies…in [a thing]…as the sum
and unity of opposites…. [E]ach thing (phenomenon, process, etc.)…is
connected with every other…. [This involves] not only the unity of
opposites, but the transitions of every
determination, quality, feature, side, property into everyother….

"In brief, dialectics can be defined as the
doctrine of the unity of opposites. This embodies the essence of dialectics….

"The splitting of the whole and the cognition of
its contradictory parts…is the essence (one of the 'essentials', one of
the principal, if not the principal, characteristic features) of dialectics….

"The identity of opposites…is the recognition…of
the contradictory, mutually exclusive, opposite tendencies in allphenomena and processes of nature…. The condition for the
knowledge of all processes of the world in their 'self-movement', in
their spontaneous development, in their real life, is the knowledge of them as a
unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing….

"The unity…of opposites is conditional,
temporary, transitory, relative. The struggle of mutually exclusive opposites is
absolute, just as development and motion are absolute…." [Lenin (1961), pp.221-22,357-58. Italic emphases in the original;
bold emphases added.]

"Motion is a contradiction, a unity of contradictions."
[Ibid.,
p.256.]

With respect to DM, at least, this is
largely because the whole topic has been discussed (by dialecticians) with the
utmost lack of clarity -– the work of
Graham
Priest
excepted, of course -- although it is arguable that the 'contradictions' he
focuses on aren't even 'dialectical' (on that, see
here).

In Essays Four,
Six, Eight Parts
One,
Two,
Three, and Eleven
Part One, as
well as below, I
hope to demonstrate that while DM-theorists frequently use the term
"contradiction" in their attempt to expose the alleged limitations of FL, the
vast majority of them display little or no comprehension of either
contradictions or FL. Nevertheless,
this hasn't prevented them from
claiming that their understanding of this word is superior to that of
Formal Logicians -- somewhat reminiscent of the way
Donald Trump says he knows more than the Generals and has "the best words".

Video One: Trump -- About As Believable As
DL-Fans

When They Pontificate About FL

According to dialecticians, the wider application of this term
allows them to account for motion and change, while those who confine
themselves to FL are unable to do this adequately -- or at all!
However, as we will see in what follows, that allegation is wildly inaccurate -- at least, with respect to
motion. Indeed, the other Essays published at this site will also show that not only can
DL not
account for change itself, dialecticians struggle to account for something as
mundane as a bag of sugar!

Clearly, the term "contradiction" is employed in FL in a
technical sense, and in a way that is widely misunderstood by DL-fans. [More on
this in Essays Four, Eight Parts
One,
Two,
Three, and Eleven
Part One.]

As far as ordinary language is concerned, one
of the ways in which we can speak about change involves employing a linguistic rule --
which many misconstrue as a logical truth
(i.e., the LOC) -- that enables us to draw certain inferences (should we choose to do so) from
what might appear to be contradictory propositions. If two putatively
contradictory sentences are held true at different times, then (given certain
other constraints) speakers of that language would normally conclude that the subject of
those sentences (if there is one) had changed. For instance, consider the following:

A change like this would usually be recorded more directly,
either by the use of a tensed verb or by the employment of some form of paraphrase, as in: "NN has joined Respect", or "NN wasn't in
Respect last year, but now she is", etc. This means that such apparently
contradictory sentences -- coupled with a wider use of the negative particle (in
all its forms) and the
rich vocabulary
we have available to us (i.e., verbs, adjectives and adverbs) -- are integral
to our ordinary notion of change. This alone shows that the claim dialecticians
make that ordinary language and FL can't cope
with change is the opposite of the truth.

Of course, all this is rather obvious -- but,
it seems that it is so blatantly obvious that DM-fans regularly misconstrue it, or
worse, totally ignore it.

[Naturally, the above was written before
Respect
self-destructed back in 2007! It is now called the Respect Coalition.
It is also worth pointing out that the above isn't the only way we can speak
about change in ordinary language! On that, see
here.]

In
which case, the idea that ordinary language and FL can't account for change is bizarre. In fact, without
the resources available to us in the vernacular, human beings wouldn't be able to
conceptualise change at all.

[And
that comment applies equally well to scientists and dialecticians. Again. ordinary language
is capable of handling change far
better than the obscure and wooden terminology invented by metaphysicians, and
especially that concocted by Christian Mystics like Hegel. On that,
here.]

In that case, if, by their use of language, dialecticians actually
end up undermining the vernacular, their theory can't fail to be problematic, if not incomprehensible --, which is
indeed what this Essay
will demonstrate (at least with respect to the their 'analysis' of motion).

Now,
as far as FL is concerned, two propositions are contradictory just in case they
can't both be true and can't both be
false at once. [The latter condition is almost invariably ignored by DM-critics
of FL i.e, that two contradictory propositions can't both be false). Some deny there is a genuine distinction here
(happily confusing inconsistencies with contradictions), even after it has been pointed out to
them! In fact, they tend to call such fine distinctions and careful attention
to detail "pedantry",
or they declare them "merely semantic".
The profound dialectical confusion that results if such distinctions are ignored can be
seen in
all its glory,
here.
Its importance will emerge as this Essay unfolds.]

Naturally, when
two contradictory propositions are conjoined -- as in ¬(p
& ¬p) --, this represents the
simplest form of contradiction in FL (and, in many cases, ordinary language).

[The difference between "contradictory" and "contradiction",
also
ignored by DM-fans, is explained
here.]

[In the above, "(E...)" is the existential
quantifier;
"↔"
is a biconditional sign (and stands for "if and only if"); "(x)" is the
universal quantifier; "&" stands for "and"; "v" is the inclusive "or"
(i.e, "and/or"); "¬"
stands for the negation operator ("It is not the case that...");
"→" is
the conditional sign (i.e., "if...then"); "p", "q", and "r" are propositional
variables; "F" and "G" are one-place,
first-level predicate letters; and "x" is a
second-level predicate-binding variable. (More details
here, and
here.)]

C1 reads: "It isn't the case that [(if
p then q
or if p then r) if and only if (if p then q or r)]."

C2 reads: "It isn't the case that [(there isn't
something which is F and not G) if and only if (everything which, if it is
F,
is also G)]."

C2a:
"It isn't the case that [(there isn't
anything which is F and not G) if and only if (everything which, if it is
F,
is also G)]."

These are, of course, just two of the potentially infinite number of logical
contradictions which can be generated in MFL. DM-theorists would be hard-pressed
to find space -- even in their quirky universe -- for
contradictions like these (once they have been
interpreted).

Moreover, dialecticians often conflate the LEM, the PB,
propositional bi-polarity, and the LOC
with one another
--
and, what is more, all of them with opposites,
inconsistencies, absurdities, contraries, paradoxes, puzzles, quandaries, oddities, irrationalities,
oppositional processes, antagonism, forces, events that go contrary to expectations,
alongside a whole host of other idiosyncrasies. In
fact, they are so eager to see contradictions everywhere, that they find they
have to tinker with the
meaning of "contradiction" so that (for them) it becomes synonymous with "struggle",
"conflict", and "opposition".

[More details on these and other dialectical confusions
and convolutions are given
in Essays Four,
Six, Eight Parts
One,
Two and
Three, and Eleven
Part One.]

A
typical example of
DM-proflicacy in this respect surfaced in a letter
sent to Socialist Worker at the end of August 2011:

"I'm
writing regarding Charlie Hore's article on economic growth during the reform
period in China (Socialist
Worker, 20 August). It
doesn't mention the powerful contradictions that emerged within the ruling
bureaucracy as a result of the reforms. Not all
sectors of the bureaucracy have benefited from the reforms. There has
been a shift from ideological campaigns towards a performance-based notion of
state legitimacy. This has
meant that many officials have experienced anxiety about their relevance in
Chinese politics and have been dragged into protest movements. A
socialist analysis has to make sense of these contradictions."
[Bold emphasis added. Paragraphs merged to save space.]

So, tensions within the communist hierarchy are
'contradictions', are they? But, no one ever explains why such things should be
called "contradictions" when they are obviously far better described as "tensions" or
"conflicts". For example, do they imply one another? No. Can one
exist without the other? Yes. This is quite unlike the alleged 'contradiction'
between the bourgeoisie and the proletariat, where one supposedly implies the
other and where neither can exist without the other.

Some might
conclude that this is just another example of Ms Lichtenstein's pedantry,
but that isn't so. [On 'pedantry', see
here.] There are
important political reasons for rejecting the use of "contradiction" in
the way it is used by Dialectical Marxists. [On that, see Essay Nine
Part Two.]

Specifically:

(1) It 'allows' dialecticians to argue
in favour of anything they like
and its opposite
(often this is done by the very same dialectician, on the same page or
in the same speech!), no matter how
anti-Marxist or counter-revolutionary this "anything" might prove to be.
These are then often 'justified' on the basis that since everything is 'contradictory',
and a 'unity of opposites', Marxist theory and practice should be contradictory,
too!

(2) It is used to
rationalise a whole raft of
substitutionist tactics, strategies and moves on the basis that even though Marx insisted on the self-emancipation of the working class, we can
substitute one or more of the following for the proletariat: (i) The Party, (ii)
The Red Army, (iii) 'Third World' guerrillas, (iv) 'Progressive' nationalists, (v)
Students, (vi) Sympathetic, left-leaning politicians, and/or (vii) An assortment of social forces,
'rainbow coalitions',
and groups,
no matter how contradictory this might otherwise seem. And concerning those who
might object..., well
they just don't 'understand' dialectics,
or, indeed, the 'contradictory' nature of Marxism, the class war, the former USSR..., etc., etc.

(3) The use of this word 'allows' DM-fans to look at the
protracted failure of Dialectical Marxism and fail to see it for what it is:
a
long-term and profound refutation
of their core theory, 'Materialist Dialectics'. It also
'allows' them to interpret
this abysmal record as the
opposite of what it is -- on the grounds that
appearances 'contradict' underlying 'essence'. So, if Dialectical Marxism looks
hopelessly unsuccessful, a catastrophic failure, the opposite is in fact the case.
This then encourages dialecticians to stick their heads in the sand while our
movement slowly runs into those very same dunes.

So, this isn't 'pedantry',
nor is it merely 'academic' point-scoring; this
word has had, and still possesses,
disastrous political implications.

[I present many more examples of the odd things DM-fans say about
their 'contradictions' in Essay Eight Part Two --
here and
here, for instance.]

Be this as it may, DM-theorists themselves would be the
first to point out
that their interest
lies not so much with contradictory propositions as it does with real materialforces,
which express, or even constitute, conflicts in nature and society
(but only if they have beenconfirmed in practice). Furthermore, since the
vast majority of classical DM-theorists believe that reality itself is fundamentally
contradictory, then, according to them, propositions which accurately describe the world ought to be
contradictory, too -- i.e., they shouldreflect
the contradictions that exist in nature and society.

But, because (contradictory) propositions are, manifestly, linguistic expressions
they
plainly aren't material forces, as such. This must mean that they aren't oppositional per se -- even though they
supposedly
reflect, or can be used to reflect (at some level), the dynamic nature of reality
--
again, according to dialecticians.

On
the other hand, even if contradictory propositions were oppositional,
they would only be so in a
derivative sense. In any case, the idea here appears to be
that while objects and processes in nature are contradictory (or their
inter-relationships are) and subject to
change, any use of language aimed at depicting reality must reflect this
accurately and adequately if it is to be
both accurate and objective.

Or, so a (very brief) case for the defence might
proceed.

However, the principles that underlie FL merely commit us to the
view that two contradictory propositions can't both be true and can't both be
false at the same time. Hence, on this basis, any claim that two
supposedly contradictory propositions can be, or, indeed, actually are both true at once (or
can be, or are both
false at once -- as noted above, dialecticians appear to be unaware of the
latter caveat) would automatically be regarded as mistaken
or confused in some way.

Indeed, that fact alone
would provide
sufficient grounds for questioning whether one or both of a pair of
allegedly true 'contradictory' propositions on offer were in fact propositions
to begin with. If it is unclear what is being proposed (in the sense of "putting
something determinate up for consideration"), then anyone attempting to do
this can't be
proposing anything determinate -- that is, this side of their words being disambiguated
-- any more than someone can open and shut that door at the same time.
[Examples of this strategy are given below, and later in the main body of the Essay. See also
here.]

Be this as it may, several factors might contribute to this
apparent impasse: (a) The
said 'propositions' could contain typographically similar words that have
different
denotations; (b)
They could be using ambiguous, vague, or figurative expressions; (c) They might be drawn from different areas of discourse;
or (d) The might have been taken out of context -- and
so on.

Based on one or more of the above, the presumption would always be that both 'halves' of an alleged
contradiction could only be held true by someone in the grip of some form of
linguistic or interpretative confusion. 'Contradictions' that have been
generated in this way wouldn't normally be regarded as capable of revealing
fundamental truths about reality; they would perhaps convey more
about the linguistic naivety of anyone so easily bamboozled.

In that case, the disambiguation or clarification of these alleged 'contradictions'
should
be expected to eliminate the 'problem'. Only an exceedingly naive person (or
worse, a Mad Dog
Idealist, like Hegel) would conclude that just
because certain 'concepts', or sentences, appear to be contradictory, nature
and society must be contradictory,
too.

Indeed, the above austere approach to what appear to be contradictions should recommend itself to materialists; not only was the
alternative view (that there are 'contradictions' in reality)
invented by card-carrying mystics, it 'implies' that the natural world possesses properties
that are only rightly
to attributed to human beings
-- i.e., the ability to converse, argue, and disagree -- i.e.,
they cancontradict one another.

In addition, and to its credit, this austere approach
undermines the traditional doctrine that fundamental aspects of reality may
be inferred solely from the logical properties of language -- or, rather, in this particular case,
that
they can be derived
on the basis of a series of
sophomoric errors concerning the nature of contradictions
(outlined a few paragraphs back, but in much more detail,
here).

Naturally, DM-apologists will view claims like these with some suspicion;
indeed, they might even appear (to them) to be dogmatic and aprioristic.
Furthermore, it
could be argued that this obsession with the fine detail of linguistic usage itself collapses into LIE, since it presumes to offer a
linguistic solution to what is in fact a philosophical,
scientific or practical problem.

However, the opposite of this is in fact the case; the approach adopted here
seeks to undermine the traditional, metaphysical dogma (which
dialecticians
themselves have
appropriated) that
fundamental truths about reality may be inferred solely from
language and 'thought' -- or even from certain 'concepts'. Clearly, is the world (or,
rather, our appeal to the
facts) that makes what we say
true or false; it isn't what we say, or how we say it, that determines the nature of reality,
or which dictates to nature and society what they must be like.
It is that approach, the traditional view of philosophical 'knowledge',
that is associated with Idealism:

"A consistent materialism cannot proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphases added.]

[As Essay
Seven shows, DM-contradictions can't be
confirmed in, or by, experience, nor can they be
verified in any other way. (The allegation that this view of confirmation,
coupled with the emphasis placed on it in these Essays, smacks of 'positivism', or
even 'empiricism', has been batted out of the park,
here.) In Essay Twelve, the ideological motivation
underlying the
contrary view will be exposed for what it is: a form of LIE itself (summary
here).]

Nevertheless, it is important to be able to recognise when the descriptive,
representational,
and expressive capacities of language begin to break down. This is relevant with respect
to the full range of DM-theses -- since they break down alarmingly quickly; indeed, when examined
closely, they invariably turn out to be either hopelessly vague, terminally
confused,
non-sensical and
incoherent -- as several Essays posted at this site have demonstrated.

Moreover, it is equally important to be able to distinguish
spurious pictures (or, indeed, non-pictures) of reality from the genuine article. DM-theorists
themselves attempt to do this when they highlight the confused, or self-contradictory,
nature of rival theories, and advocate their rejection on that basis.
[This allegation is substantiated in Essay Eleven
Part One.]

On the other hand, DM-theorists believe that their analysis begins
with reality (albeit 'mediated' by the conceptual or practical resources available to
human beings at any given time). They then require that our linguistic resources
are adapted, even upgraded, accordingly. On this view, if nature is contradictory and ordinary
language and FL can't accommodate that fact, then that must be because they are
limited, or defective, in some way -- hence, should be supplemented with concepts drawn from 'Materialist Dialectics', or even
from Hegel, himself (albeit, put 'back on their feet').

It isn't easy for a response
to, and refutation of, this to appear un-dogmatic.
Language has been moulded throughout history by an evolving set of social
norms and conventions, which were themselves refined by factors
that were at work across different Modes of Production. Because of this, it might seem possible to
argue
that, when faced with situations that appear to be 'contradictory', human beings not only could,
they actually did, develop and then adopt dialectical categories or
concepts.

[However, the 'factual basis' underlying that
supposition will be seriously undermined in Essay Fourteen Part One (summary
here), and
briefly below.]

Even so, given other conventions that were in
fact adopted -- that is, in practice; no one supposes that overt decisions
were taken here --, the above scenario is extremely unlikely.

As the word itself suggests,
to contradict someone is to gain-say or deny that what they have uttered is true (or
false, as the case may be). So, if NN says it is raining, and MM
says it isn't, then (all things being equal) they would be contradicting one
another. Furthermore, this isn't affected in the slightest by either one of the following
being the case (in the vicinity of these interlocutors): (i) It is
pouring down with rain, or (ii) It is dry as a bone.

Whether or not "It is raining" is actually true in no way affects the fact that
these two sentences are contradictory. All that is required is that
if one of them is true, the other is false, and vice versa. We
wouldn't be able to understand anyone who
claimed that bothNN and MM were mistaken. Fanciful circumstances to one side
(which was partially the point of the "all things being equal" clause, above), how is it possible for it to be
false that it is
raining andfalse that it isn't raining at the same time and in the same
location?

Some might point to the vagueness of
sentences like "It is raining". This would seem to mean that both of the above could in
fact be false, since it might be indeterminate whether it is raining or not
(perhaps the weather is clearing up, so that anyone who said it was raining
would be wrong, just as anyone who said it wasn't would be, too). To be
sure, sentences like these are vague, but just as soon as it had been decided
that it is actually raining, then just one of the following sentences would be false
and the other true: (a) "It is raining", (b) "No, it isn't raining". The same is the case in reverse
-- i.e., if it had
been decided that it isn't in fact raining: one of (a) or (b) would be false,
but no both. In circumstances like these, we wouldn't be able to make sense of anyone who said both were false, or
both were true.

But, what if we can'tdecide whether or not it isn't raining?
In that case, these sentences would be neither true nor false until a
decision had been made either way. In such circumstances, they would fail to
be
propositions until this had been resolved. If we can't decide when it is raining or when it isn't then nothing determinate will have been proposed
(i.e., put forward for consideration) by saying it is, or by saying it isn't. I am of
course speaking about aradical failureto decide, here, that is, where no
one could decide, even in theory, whether or not it was raining in the
vicinity of those attempting to decide. If it
were in principle impossible to decide in such cases, then there would be
no point to uttering such sentences, and they wouldn't have entered the language.
It is raining" would lack
both a
sense and a use.

However, in what might be described as
non-radical circumstances, where it still can't be decided whether or not it is
training for contingent reasons -- maybe the interlocutors in question are
trapped underground, are locked away in a dungeon, can't see outside, or are
unable to receive
any information from the outside for whatever reason -- then these two
sentences would still be contradictory, since if one of them were true
(whether or not this fact is known) the other would automatically become false.

However, in everyday life (i.e., outwith the use of aesthetic, ethical,
political and religious
vocabulary (etc.), where the meaning of words is often "essentially
contestable"), these sorts of problems do not normally arise. When in
doubt, we say things like "It's trying to rain...", "It's spitting, I
think...", or "I reckon it's clearing up...". Only a hardcore
contrarian
would come out with statements like "It is and it isn't raining" -- perhaps on the basis that
there are gaps between the raindrops, or because it is raining in the
vicinity, but not, say 100 metres down the road, or in the next county. If someone
were consistently to adopt this approach to all such sentences,
they would either have very few friends or they would enjoy a severely limited social life
-- either that, or they would be diagnosed with a
Personality Disorder of some sort. And, if we all adopted such an
attitude, inter-communication would grind to a halt. [On that, see also
here.]

It is
also worth adding that
contradicting someone could be
challenging a truth, and not always confronting falsehood, as many
suppose.

It could be objected that it was earlier claimed that:

...if NN says it is raining, and MM
says it isn't, then (all things being equal) they would be contradicting one
another. This isn't affected in the slightest by either one of the following
being the case (in the vicinity of these interlocutors): (i) It is
pouring down with rain, or (ii) It is dry as a bone.

Whether or not "It is raining" is actually true in no way affects the fact that
these two sentences are contradictory.

When it was asserted a few paragraphs later:

But, what if we can'tdecide whether or not it isn't raining?
In that case, these sentences would be neither true nor false until a
decision had been made either way. In such circumstances, they would fail to
be
propositions until this had been resolved. If we can't decide when it is raining or when it isn't then nothing determinate will have been proposed
(i.e., put forward for consideration) by saying it is, or by saying it isn't. I am of
course speaking about aradical failureto decide, here, that is, where no
one could decide, even in theory, whether or not it was raining in the
vicinity of those attempting to decide. If it
were in principle impossible to decide in such cases, then there would be
no point to uttering such sentences, and they wouldn't have entered the language.
It is raining" would lack
both a
sense and a use.

Which is it to be? If we can't say whether sentences like
these are true or if they are false, then how can they be contradictory?

The objector forgot to quote this caveat:

All that is required is that if
one of them is true, the other is false,
and vice versa.

And we can arrive at
that conclusion well in advance of knowing whether one of
them is in fact true, or whether one of them is in fact false. As noted below,
this capacity is based on rules we have for the use of the negative particle,
and, as with any rule, it is possible to decide how that rule can or can't be applied in
advance of actually applying it. For instance, we can decide what would, and
what would not, count as offside in football (soccer) even if there is no game
actually being playedat the time, and even if no more gamesare ever played
--, and even if, during a game, we lose sight both of the pitch and
the alleged offence itself (if the pitch is fog bound, for example). Plainly,
that is because rules aren't capable of being true or false themselves; they are practical or impractical, applied or mis-applied,
useful or useless, etc. Hence, this
particular rule is independent of any alleged truth or falsehood, as such.

This topic is, of course, connected with the so-called 'Law of
Excluded Middle' [LEM], as it is supposed to feature in ordinary discourse. In
that case, some
might be tempted to agree with Hegel when he asserted the following:

"Instead of speaking by the
maxim of Excluded Middle (which is the maxim of abstract understanding) we
should rather say: Everything is opposite.Neither in heaven nor in
Earth, neither in the world of mind nor of nature, is there anywhere such an
abstract 'either-or' as the understanding maintains. Whatever exists is
concrete, with difference and opposition in itself. The finitude of things will
then lie in the want of correspondence between their immediate being, and what
they essentially are." [Hegel
(1975), p.174;
Essence as Ground of Existence, §119.
Bold emphasis added.]

To which Engels added this oft quoted gloss:

"To the
metaphysician, things and their mental reflexes, ideas, are isolated, are to be
considered one after the other and apart from each other, are objects of
investigation fixed, rigid, given once for all. He thinks in absolutely
irreconcilable antitheses. 'His communication is "yea, yea; nay, nay"; for
whatsoever is more than these cometh of evil.' [Matthew
5:37. -- Ed.] For him a thing either exists or does not exist; a
thing cannot at the same time be itself and something else. Positive and
negative absolutely exclude one another, cause and effect stand in a rigid
antithesis one to the other.

"At first
sight this mode of thinking seems to us very luminous, because it is that of
so-called sound common sense. Only sound common sense, respectable fellow that
he is, in the homely realm of his own four walls, has very wonderful adventures
directly he ventures out into the wide world of research. And the metaphysical
mode of thought, justifiable and even necessary as it is in a number of domains
whose extent varies according to the nature of the particular object of
investigation, sooner or later reaches a limit, beyond which it becomes
one-sided, restricted, abstract, lost in insoluble contradictions. In the
contemplation of individual things it forgets the connection between them; in
the contemplation of their existence, it forgets the beginning and end of that
existence; of their repose, it forgets their motion. It cannot see the wood for
the trees.

"For
everyday purposes we know and can say, e.g., whether an animal is alive or not.
But, upon closer inquiry, we find that this is, in many cases, a very complex
question, as the jurists know very well. They have cudgelled their brains in
vain to discover a rational limit beyond which the killing of the child in its
mother's womb is murder. It is just as impossible to determine absolutely the
moment of death, for physiology proves that death is not an instantaneous
momentary phenomenon, but a very protracted process.

"In like
manner, every organic being is every moment the same and not the same, every
moment it assimilates matter supplied from without, and gets rid of other
matter; every moment some cells of its body die and others build themselves
anew; in a longer or shorter time the matter of its body is completely renewed,
and is replaced by other atoms of matter, so that every organic being is always
itself, and yet something other than itself." [Engels (1976),
pp.26-27. Bold emphases added; quotation marks altered
to conform with the
conventions adopted at this site.]

However, as I have argued in Essay Nine Part One:

Nevertheless, it is difficult to
see what Hegel was trying to say here. That is because any attempt to
interpret him requires the use of the very terms he claims are misleading. The
construal of his work requires decisions be taken about whether he meant either this
or that by what he actually wrote. If an author always
means both (or maybe even neither) then interpretation is rendered impossible and any attempt to unravel
their meaning becomes self-defeating (as we are about to see).

So, if Hegel were right, if absolutely
"everything is opposite", and there is no "either-or"
anywhere in the universe, it would be impossible
to disentangle what he meant from what he didn't, since we would be unable to
decide whether he believed of, say, any two sentences "P" and "Q" one or more of
the following:

H1: (i) Both P and Q;
(ii) either
P or Q; (iii) neither P nor Q; or (iv) either P or Q, but not both.

But, if,
say, P and Q were
inconsistent (that is, if,
for instance, Q implies not P, or vice versa -- I give
an example, below), and we interpreted his words one way (perhaps
that he believed both P and Q,since to do otherwise
would involve the use of the dread 'either-or'),
then we would have to conclude that he accepted
both as part of the "unfolding of truth" (as he might have put it), which would
mean by his own lights, of course, that we would be unfolding error instead!

Hence, in order to reject one or other of these two options, we would be
forced to appeal to the "either-or" -- that is, we would have to conclude that
Hegel accepted P or he accepted Q, but not both.

However, if we were to remain true to Hegel's dictum --
that"neither in heaven nor in
Earth, neither in the world of mind nor of nature, is there anywhere such an
abstract 'either-or' as the understanding maintains" --, then we would have to
conclude he accepted both.

So, any attempt made
now to specify exactly what Hegel meant would undermine what he actually
said about the use of the "either-or of understanding", for we would have to
accept that Hegel asserted one thing (P), or he asserted something else (Q), but not both. Without this assumption it would become
impossible either to comprehend or defend him. If Hegel genuinely
cast doubt on the "either-or of understanding" (and he wasn't being
deliberately enigmatic, disingenuous, mendacious, or merely playful) -- and assuming he was correct to do so
--, then any attempt to
interpret him as asserting Por asserting Q would have to
conclude that he asserted both. [Again, I give a clear example of this, below.]

In that case, any
determinate interpretation of
Hegel would have to ignore his own advice, and reluctantly accept
the deliverances of the "either-or" of ordinary language (or
'commonsense', along with its
corollaries), and acknowledge that, concerning either P or Q, he believed only one, not
both.

Here, truth would advance --
with yet another
dialectical
inversion -- by forcing us to disregard Hegel!

In order to make this more concrete, let us
suppose that:

"P" is: "Neither
in heaven nor in Earth, neither in the world of mind nor of nature, is there
anywhere such an abstract 'either-or' as the understanding maintains",

and,

"Q" is: "There is in fact an abstract
'either-or' somewhere in the world of mind or of nature (etc.)."

Now, either Hegel accepted Por he accepted
Q -- which would, of course, imply that there is at least one 'either-or' "in heaven or
in earth (etc.)" -- i.e., here, right in front of us, right here, right now!

On the other hand, if
he (or we!) took his advice and accepted
bothPandQ, rejecting this annoying "either-or", then not much sense could be made of what he was
trying to say.

Incidentally, the above criticism
isn't
affected by Hegel's own interpretation of these controversial words (nor any
technical meaning his epigones might want to attribute to them, since they, too,
would have to conclude that he meant this or he meant that, not both), but solely concerns
how we are to understand him now, in this world, by our perusal of
those very material words (in print, or on a screen), quoted earlier.

Hence, it is beside the point whether
the rationale for his own (dialectical, then speculative criticism) of the use of
such words by the "abstract understanding" is legitimate or not (irony intended). Since Hegel's writings
appear before us now as phenomenal objects, given also that they aren't
self-interpreting (when we recall that Hegel is no longer with us to explain himself --
but, even then we would have to accept he meant either PorQ, not both), they face the ordinary cannons we employ elsewhere to
understand anyone's words. In order to read and perhaps interpret Hegel as
believing this or that, but not both, we are forced to
ignore his advice and employ the dread "either-or".

Naturally, this is just one more reason why
ordinary language can't be by-passed, or undermined, no matter which 'genius'
cons some of us into thinking otherwise.

Once again, it is little use complaining that
this is not how Hegel wanted his use of the "either-or" of "understanding"
to be interpreted (i.e., ironically, that is, that we view it this way but not that),
since he
himself holed that complaint well below the water line when he
asserted:

"Instead of speaking by the
maxim of Excluded Middle (which is the maxim of abstract understanding) we
should rather say: Everything is opposite.Neither in heaven nor in
Earth, neither in the world of mind nor of nature, is there anywhere such an
abstract 'either-or' as the understanding maintains. Whatever exists is
concrete, with difference and opposition in itself. The finitude of things will
then lie in the want of correspondence between their immediate being, and what
they essentially are. Thus, in inorganic nature, the acid is implicitly at the
same time the base: in other words, its only being consists in its relation to
its other. Hence also the acid is not something that persists quietly in the
contrast: it is always in effort to realise what it potentially is." [Ibid.]

Hence,
if "everything is opposite",
and Hegel's works were written somewhere on this planet, and copies of them still take
on physical form in this universe(!), then anything he committed to paper must be its own opposite,
too -- or, he was wrong.

[Irony intended again.]

In
either case, it would be
foolish to believe Hegel was serious (or, and what is far more likely, that he had thought things through with
due care) when he wrote the above words, while also accepting what he said about
the LEM -- the
dread "either-or".

So, and following Hegel's
own advice,
the above passage should in fact be re-written along the following 'Hegelian' lines:

"Instead of both speaking and
not speaking by the maxim both of Excluded Middle and not Excluded Middle and
(which is and is not the maxim of abstract understanding) we should and we
shouldn't rather say: Everything is, and some things are not, opposite. Neither
in heaven nor in Earth, and both in heaven and in earth, neither in the world of
mind nor of nature, and both in the world of mind and of nature, is there
anywhere such an abstract 'either-or' as the understanding maintains, but there
is, and it is everywhere, too, while it is nowhere
as well. Whatever
exists is concrete, and it isn't, with difference and opposition, and
also without difference or opposition, in itself, and in other things, too. The finitude of things will and will not
then lie in the want of correspondence, but also with actual correspondence, between their immediate being, and what
they essentially are, or are not, and, indeed, both. Thus, in inorganic nature, and
outside of it, the acid is and is not implicitly at the same time, and at other
times, the base, but it isn't the base, either: in other words, but also in the same words,
its only being, and its many other beings, consist, and do not consist, in its relation,
and absence of any relation, to its
other, and whatever isn't its other. Hence also the acid is not something, and
it is something, that persists quietly, and noisily, in the contrast, or the
accord: it is
always, and is it is never, in effort to realise what it potentially is, and what it
actually is not."

Everyday,
boring old non-abstract understanding
will, I think, readily see what arrant nonsense results from Hegel's 'genius'
when we apply his ideas to his own words -- providing we remain in this universe.

Any who object to the above re-write can, of
course, neutralise its implications by demonstrating that Hegel's work wasn't actually written
in this universe, or on real paper, but was written on Ideal paper, neither in heaven nor on earth
-- and that they themselves don't exist anywhere, either (or both, or neither), in order to do that (or not).

[On the
'acid and base'
fiasco, even should we take Hegel seriously, see here.]

In a recent book [Stewart
(1996)], a number of misinterpretations and misrepresentations of Hegel's work
were corrected by a handful of Hegel scholars. However, there would seem to be
little point to this exercise if Hegel's ideas about "either-or" are
to be believed. If he were right -- that in the entire universe there is no
"either-or" -- there would be some truth even in the wildest allegations about
him or his work.

For instance, these: that
(i) Hegel fully
accepted without question the unlimited applicability of the LOI in every
conceivable circumstance without any qualifications whatsoever (and this includes
its use in dialectical
and speculative thought as well as in relation to change, conceptual or material), and he did not; that
(ii) he flatly denied that reality or thought is contradictory
in any sense at all, and he did not; that (iii) he doubted the
truth of every single one of his own ideas all the time, and he did not; that
(iv) he wrote nothing at all in German in his entire life,
and
he did not; that (v) everything he wrote was actually written
by
Schelling
-- in fact it was published
only yesterday, and it
wasn't --; that (vi) he was a Shape-shifting Martian, and he wasn't...

[Anyone attempting to reject one or more of the above alternatives on the
grounds that Hegel must have accepted one of them, but not both -- or, indeed,
that they must do likewise -- will, alas, have to employ the dread LEM in
order to do so, vitiating Hegel's challenge, as well astheir own.]

It could be objected that this
completely misunderstands the nature of
DL as Hegel
himself conceived it. Unfortunately, even that response is framed in ordinary language-- and, it was foolishly written in this universe! --, so,
since a decision has to be taken over whether or not it is valid, a quick
reference to DL will indicate it is both.

This means that until DL-fans commit
themselves to one or other view (but not both), it is impossible even to begin to
evaluate anything they say -- and neither can they!

Unfortunately, just as soon as
DL-fans actually manage to specify what they mean
(i.e., that they genuinely intend this but not that), we must cease to take
them seriously -- since they would then have employed the dread LEM (in this
universe),
undermining their own criticisms of it!

Either way,
such defenders of Hegel may
be ignored even before they decide whether they agree with the above criticisms,
or not (or both).

It
could be objected that the above conclusions are ridiculous and do not follow
from a consistent application of the dialectical method; hence Hegel can't be saddled with any of them.

Once
more, these 'ridiculous conclusions' either do or they do not follow from what Hegel wrote. If the above
rebuttal is right, and they don't follow, then there is at least one either-or at work here, namely
this one (since both options wouldn't be correct in that case -- only one option
would be, namely that they don't follow). And, if that is so, then these
'ridiculous conclusions' do indeed follow, after all, since Hegel would in that case be
wrong to assert there is no either-or anywhere in existence when one such
has just been used to reject one option in favour of the other.

Hence, taking each 'ridiculous conclusion',
one at a time, if we maintain it doesn't follow, then we will have applied the
LEM once more -- in that we would thereby have denied that that particular 'ridiculous
conclusion' both does and does not follow, and thus that one of these either-or
options must obtain --, and we arrive at the same result.

The problem with sweeping claims like
these (which litter Traditional Philosophy, and not just Hegel's ill-considered
work) -- in this case, concerning the supposed limitations of certain principles of
FL (and especially
those that express patterns of inference mirrored in our use of ordinary language, such as the
LOI, the
LOC and the
LEM) -- is that they
invariably collapse into incoherence, as we have just seen.

Which is why, once again, we can say with
complete confidence that no one (not even Hegel) could possibly understand Hegel!

It is
of course possible to 'adapt' Engels's comments in like
manner to take account of his own advice (but to save the reader's sanity, this
has been inflicted on only half of his words):

"At first sight and not at first sight,
this mode of thinking and of not thinking seems, and it doesn't seem to us, and not to us,
very luminous and not at all luminous, because it is and it isn't that of so-called
sound common sense and not so-called common sense. Only sound common sense, and
anything other than common sense, respectable fellow that he is and isn't, in
the homely realm of his own four walls and outside them too, has very wonderful
adventures and slightly non-wonderful adventures directly he ventures out into
the wide world of research, or not...."

So, not even Engels could have taken his own advice and hope to
have made sense.

[Incidentally, his argument concerning the status of living organisms is
destructively analysed
here and
here.]

Any who still have doubts, try them out on sentences like the
following (i) "The Nile is longer than the Thames" and (ii) "Nile isn't longer than
the Thames"; (iii) "Hitler was a Nazi", and (iv) "Hitler wasn't a Nazi". Now, can both
of (i) and (ii) or both of (iii) and (iv) be true at once or false at once?

Finally, someone might object that an earlier example (concerning off-side in
football (soccer)) in fact underlines the limitations of FL. In a live game,
many players (in or near an off-side position) are moving, and at any point they
might be in a borderline position between on-side and off-side. FL insists it is
an "either...or" here, when it is often a "both...and". Admittedly, on occasion
even those with access to video evidence can't decide, or they have differing
opinions. Of course, that doesn't affect the observation that when it is
decided that the player concerned is off-side, it then becomes false that he/she
isn't off-side.

What
if it can't be decided? But, decisions are always made. Never in the
history of the game has it been left hanging without a decision (in such
circumstances). That decision will make one proposition true -- "NN is
off-side" or "NN isn't off-side" -- and the other false. At no point
would anyone come out with "NN is on-side and off-side!"; not
even a referee who was also a DM-fan. And that will still be the case even
if those reviewing video evidence disagree. Someone will arbitrate here (the
third referee, perhaps?) and a decision will be made.

[Graham Priest has tried to are that there are states of affairs in such fluid
circumstances where it is true to say an object is in both states. I have
discussed this response in Note 18a.
Readers are directed there for more details.]

So, the facility we have in language (which apparently goes back as far as records last,
or as far back as human beings have been able to argue -- indeed,
without it, we wouldn't be able to comprehend indicative sentences before we
knew whether they were true or whether they were false (why that is so is
explained in detail in Essay Twelve
Part One)) -- this facilitymeans that our ancestors clearly failed to take the
DM-route. And it isn't difficult to see why. In fact, given the linguistic practices we now have
(and the social relations from which they have arisen), it is impossible to make sense of
the claim that a contradiction could be true (or, rather, that two
contradictory propositions could both be true or could both be false at once -- that is,
without (retrospectively) altering the meaning of the word "contradiction" itself). Indeed, we would fail to
comprehend anyone who claimed that in a dispute (where someone gain-said what
someone else had asserted) both sides could be speaking the literal truth --
ambiguous examples excepted, of course.

[In order to prevent the account presented here sliding into some
form of Linguistic
Psychologism, it should be read in conjunction with the careful
distinctions set out in Shanker (1998), particularly Chapter Three, and
especially pp.97-120. Of course, there is nothing wrong with employing the word
"contradiction" in novel ways, but that having been done, any such new uses can't
affect its current, ordinary employment, nor can it be related to it, let alone
to its role in
FL.]

In cases where disputants might appear to be doing this
(i.e., where both parties to an argument are gain-saying one another, but where
both also seem to be speaking the literal truth), the most
likely response would be to try to disambiguate their
words in order to resolve the serious problems that 'true contradictions' would
create in everyday life.

And this can be asserted with some confidence
because, as noted above, the conventions we now have prevent us from
understanding how a contradiction could be true (or, rather, how two
contradictory propositions could both be true or both be false, at once). Not only that,
but, these
conventions prevent
us from understanding anyone who might think otherwise. Even worse still, they also
prevent us from now understanding how humanity could ever have developed
alternative conventions, or how we could make sense of anyone who supposed that they
might have.

This is one intellectual river we can't now step
back into, even
once -- to paraphrase
Cratylus.

In fact, these observations are connected with: (i) The way that negation works
in language, and (ii) The capacity language has of allowing us to understand an empirical
proposition (i.e., a fact-stating indicative sentence) before we know whether it is true or
whether it is false. [More on that in
Essay Twelve Part One.]

[Incidentally, I have added the following codicil: "Or, rather,
how two contradictory propositions could both be true or both be false, at
once",
since most logicians (particularly mathematical logicians) regard contradictions
as false, whereas if the
LOC is a rule of language (or, even better, the LOC is an indirect expression of
the rules we have for the use of the negative particle), and not a logical truth,
a contradiction in language can't be true or false. If a contradiction
could be false, then it could be true (for reasons explained in Essay Twelve
Part One), which would create
problems for how we use the negative particle. It is far better therefore to regard
contradictions as senseless. (The word "sense", as it is used in most of
these Essays, is explained here.)
Of course, this view might create problems for the
Truth Tables,
but this can be overcome by a stipulation to the effect that in FL, a
contradiction is always given the value "F". (This ad hoc
stipulation shouldn't worry logicians since they have a similar stipulation that
the identity relation is given the value "True", but for no good reason.)]

The above assertions might seem as
dogmatic as they are controversial
(i.e., to DM-fans), so I shall now defend each in turn.

Take the first of these -- which was that we should fail to understand
anyone who believed a contradiction could be true (or, rather, how two
contradictory propositions could both be true or both be false, at once), and that we would seek to
disambiguate it (or them) in order to make sense of what it or (they) said. Consider the following example:

Let us suppose someone asserted that both B1a and B1b
were true. Faced with this, we would find it difficult to take this person, or what
they said either literally or seriously; that is because both halves of
B1 (i.e., B1a and B1b) couldn't be true,
nor could they both be false.

[Some might think that these are not the type
of contradictions that are of interest to dialecticians; that objection will be
dealt with
below.]

However, if
both B1a and B1b were still held true, then, trivial cases aside (such as
the names "John Rees" and "The
Algebra of Revolution"
didn't
refer to two separate individuals or books) we could only make sense of the
contradiction they seem to express by noting the ambiguous use of the word
"write". In one sense of that term it would imply that John Rees was the author of the
said work; in another quite ordinary sense it might suggest that the book wasn't hand-written, but was perhaps word-processed. [Or, even that Rees had
used an
amanuensis.] In that case, B1 would
be expressing the fact that although John Rees authored the said book he did not hand-write
it (or did not hand-write it himself). It would then be clear that B1
only appeared to be contradictory because of this elementary equivocation. We
wouldn't automatically think that there were real material forces at work behind
the struggle to produce this book -- no matter
how well-confirmed each half of B1 happened to be.

[This shows that an
empirical check in such cases isn't relevant to what is in fact a logical
or conceptual issue.]

Again, someone might object, arguing that the above
argument reveals the LIE implicit in the logical caveats this Essay
has expressed, for
it seems to restrict the options available in nature and society by appealing to controversial logical
or linguistic pre-conditions.

But, that would be to mistake the approach adopted here for its opposite. The
strategy employed at this site seeks to undermine the idea that substantive truths about
reality can be derived
from logical, conceptual or even contingent features of language. It does this
by basing itself on what
we would now try to do (prior to, and independently of, the adoption
of a pet theory) to
interpret or understand what appear to be contradictions as and when they
might arise. In that case, these Essays appeal to rules (i.e., the linguistic
expression of normative social practices) we already use
(or with which we
comply), not to a series of truths
that can be inferred from a misconception of their nature.

Indeed, it is the opposite (dialectical) view that collapses into LIE, for it confuses
linguistic and logical rules with empirical -- or, what are in effect
Super-Empirical -- truths. In DM, this
occurs when, for example, dialecticians
treat the LOC as a truth,
which they think could be (and often is) false -- or which is at least only true
'within certain limits'. Their criticism of the LOC leads them to argue that
contradictions themselves can be true (or, that they can and do exist). But, if, as noted earlier, the LOC is in fact a rule (or if it
expresses a rule we ordinarily use in relation to specific uses of the negative
particle), it isn't the sort of thing that can be either true or
false -- any more than orders or questions can be true or false.

[Further ruminations on this theme will be resumed in Essay
Twelve Part One, where it will be
argued in detail why the aforementioned confusion of rules with substantive
truths about the world is a characteristic feature of Traditional Thought. That
is because this ancient approach to philosophical
'knowledge' is predicated on the idea that there is a hidden world --
anterior to experience --, accessible to thought alone. It is from such
ideologically-inspired confusion that Metaphysics (and now dialectics) originally
arose.]

Admittedly, B1 is glaringly trite, but it was deliberately chosen so that the
strategy of disambiguation would be clear to all.

B1:
John Rees wrote and did not write The Algebra of
Revolution.

Nevertheless, and
against this, it could be objected that DM-theorists are more
concerned with the study of real material forces operating inside
Capitalism in order to assist in its demise. In that case,
simplistic examples like B1 are not even remotely relevant. Nor are they
even dialectical contradictions, to begin with.

Or, so it could be argued.

In order to counter this response, the sort of
contradictions DM-theorists are interested in will be analysed elsewhere
at this site (and in unprecedented
detail -- for example, here,
here and
here). There, it will be shown
that "real material contradictions" turn out not
to be contradictions to begin with (in any sense of that word -- on that, see
here and
here) -- and they can't be turned into
"real material contradictions" howsoever they are interpreted, or, indeed, 'surgically enhanced'.

With respect to the other assertion
advanced above -- that we would
fail to understand alternative conventions, given those we already have --,
the key point is that as social beings we may only succeed in understanding
something when, plainly, it is presented to us in a language and in a form with which we are
familiar; typically, but not exclusively, this takes place in ordinary
language. And that, too, can be asserted with some confidence since the word
"understand" is (patently) in ordinary language already. [The
significance of that point will emerge in Essay Thirteen
Part Three.] But,
language isn't a free-floating phenomenon; its invention and its evolution are a function of
our social, historical and technological development.In
addition, our use of language is also subject to constraints inherited
from previous generations, which we clearly had no hand in shaping.
Indeed, all of us had to be socialised (by parents, siblings, carers, teachers and
peers) into using language within, and in compliance with, these constraints. As
individuals, we manifestly didn't socialise ourselves.

Moreover, we demonstrate our mastery of this complex
socio-linguistic tool when we begin to communicate and interact with others.
While we can form thoughts as we please, we can't do so under logico-linguistic
and social conditions of our own choosing
(to paraphrase Marx).

Now, it is tempting to think that
these 'limitations' present some
sort of physical barrier -- or, at
least, that they represent merely contingent constraints on our use of language --, but that
would be a serious mistake. There are physical and contingent constraints
on language (for example, no one could utter or understand a trillion word
sentence), but these aren't the limitations intended.

[A clue to the nature of these limitations can ascertained by
anyone who reads the Essays posted at this site, especially where it has been
demonstrated time and again how quickly DM-theses fall apart, and how they can't be repaired no matter what is done
with them. That
sort of limitation isn't physical; it is conceptual. Another example can be found
here.]

B1:
John Rees wrote and did not write The Algebra of
Revolution.

Fortunately, however, the negative
criticisms of DM at this site do not depend
on the validity of this latest batch of seemingly dogmatic assertions.
Doubters need only think about how they themselves would interpret B1 (or indeed
B2, below), and these points should become a little clearer.

[Incidentally, the aforementioned "limitations" aren't those that words exercise upon us;
it expresses to how we collectively -- through our socialisation -- understand and thus
use the words
we already have. To suppose otherwise would be to
fetishise language.]

In
relation to understanding others who speak different languages, or individuals
from the past, while we can translate
what they have to say (ancient or modern)
into our own language, we may do so only within the constraints currently
operating on us and out own language -- unless we want to restrict ourselves
merely to bald transliteration.
This means that because we can't make sense of
contradictory speech now, we should find it equally difficult to
comprehend how contradictions could ever have been held true by anyone in
the past, either.

Of course, there have been mystics who professed all manner of odd
and contradictory ideas. Other than Hegel, this includes, for instance,
Buddhist logicians and 'teachers', but it is a moot
point whether anyone has ever understood the strange things they say. Indeed,
mystics themselves tell us they don't understand the conundrums they come
out with, which is part of their superficial appeal. Would anyone listen to
those pretending to transmit the 'divine word' if it were easy to understand.
Mysticism and obfuscation go hand-in-hand, as they do in DM. [More on this in Essay Fourteen Part
One (summary here).]

Even so, we are equally incapable of
translating (note: not transliterating) any language, ancient or modern, into our own in comprehensible
terms while attempting to depict its users employing contradictory speech,
all the while holding these contradictions true, or, indeed, imagining that
those who engaged in such speech held them true, too. This doesn't imply that we
have to reject the idea (as false) that such individuals actually believed these contradictions
were true, but we certainly can't hold them true. While we might acknowledge the
fact that some individuals (in the past (or whenever)) speak, spoke, or have spoken in
paradoxical ways, given what we now mean by the words we use, it is now impossible to make
sense of the supposed possibilities these ancient or mystical sayings could have presented to
those who produced them -- nor, indeed, determine whether or not they
presented anything determinate at all. Moreover, since these odd individuals invariably fail
to explain themselves, it is quite clear they
couldn't make sense of their own words either.

In like manner, DM-fans can't explain their 'contradictions', either, and
regularly complain
that critics just don't "understand" dialectics.

In which case, ifit is now impossible
to make sense ofthe possibility that individuals in the past held
certain contradictions true then we manifestly can't comprehend the
supposition that contradictions could ever have been true, whether or not
they had been viewed that way by such
individuals.

Once again, the various 'true contradictions' to which DM-theorists appeal
will be examined elsewhere at this site (for example, follow the links posted
above).
Graham Priest's much more detailed (and
logically-informed) attempt to
defend the idea that there can be, and are, 'true contradictions' in nature and
society will be examined in a later Essay. [In the meantime,
readers should consult Berto (2007), Goldstein (1992, 2004), Field (2008), and Slater (2002, 2007a), as well as
this review.]
I have, however, added a few comments to Note 18a
related to Priest's much more sophisticated attempt to show that motion and change are
contradictory; or as he puts it:

"I [have
argued in support of] the idea that contradictions not only occur in certain
sorts of change but actually are the states of change themselves." [Priest
(2006), p.172.]

Some
might take exception to the above assertions, claiming that they
can imagine speakers holding certain contradictions true (and which
contradictions do indeed represent real material forces), namely themselves! Dialecticians, it seems,
are living disproof of the sweeping assertions made in this Essay.

Or, so it could be argued.

However, this Essay aims to show that Hegel and Engels's claims
(that motion is 'contradictory') are far too vague and confused for them to be assessed for
their
truth or their falsehood (and hence that the 'contradiction' they claim to see
in moving bodies isn't one in any sense of that word). Again, other examples of dialectical 'contradictions' will similarly be
dealt with in Essays Eight Parts One, Two, Three,
and Eleven
Part One. In addition, the
DM-thesis that reality itself is comprised of countless trillion UOs will be destructively
criticised in Essay Seven
Parts One
and Three.

[UOs = Unity of Opposites.]

Hence, because it isn't possible to make sense of any of the examples of
'dialectical contradictions' offered by DM-theorists, the above
"sweeping assertions" have everything going for them. Since
dialecticians have shown that they themselves are incapable of explaining these mysterious
'contradictions' to anyone, let alone one another, that merely serves as further
confirmation. [On this, see here.]
Indeed, on Internet discussion boards, when academic Marxists and revolutionary activists
alike are asked
(often repeatedly) to explain exactly what 'dialectical contradictions' are,
to a
clone, they fail to do so, or they just ignore the question. [Links to many of these discussions
have been posted
here.]

To be sure, as noted earlier, there have been, and still are, religious believers who
assent to all manner of apparently contradictory ideas, but that doesn't refute
the above allegations. Their talk is often non-propositional -- on the
contrary, it is wall-to-wall,
incoherent
non-sense, as will be
demonstrated in a later Essay. The same comment applies to
similar ideas expressed by
Buddhists
(this links to a PDF) -- or, more
pointedly, to Zen
Buddhists --, who also seem to glory in paradox.

However, in relation to the claim that we wouldn't be able to
make sense of the possibility that there might have been past generations who
believed, or who could have believed, there were true contradictions, consider this example:

B2: This four thousand year old inscription says
that its author wrote and did not write it.

Now, despite the fact that dialecticians assure us that reality
is contradictory, not even they would attempt to understand B2 literally.
That isn't because it would be especially difficult for them to do so, but
because any claim to the contrary
would undermine the meaning of the word "literally", at the very least.

But, even supposing a few
Mad Dog Dialecticians [MDD] could be found
who did attempt to do this, they would find it impossible to explain to anyone
else in literal terms what sense they made of B2 -- other than by
disambiguating it.

As noted earlier, trite
examples like B2 were deliberately chosen to illustrate a point that is
all too easily missed: when faced with the paradoxical things people sometimes
say, we automatically make an effort to disambiguate their words or their actions;
we adopt what
Donald Davidson once called
the "principle of charity" when
attempting
to grasp their meaning and/or their intentions. [Davidson (2001).]

[Of course, in doing so, we have to distinguish between
speakers' meaning (i.e., what an individual hopes to convey or achieve by their words) and
word meaning (i.e., what those words actually mean in the language). The failure to
do so leads into the sort of confusion that undermines, for example,
Voloshinov's work, as well as that of his
epigones. (I have discussed this in extensive detail in Essay Thirteen
Part Three.)]

Hence, when confronted with someone who asserted an apparent contradiction we
would normally employ the above policy (trivial examples excepted, of course).
That doesn't mean this will necessarily distort what
an individual had said, or had written; rather, it is that we wouldn't be able to
understand such individuals if we didn't do this.

In any case, if there are any MDDs out there (that is,
DM-supporters who reject some or all of the above points), they would be hard-pressed to explain to anyone else
what they themselves took the sense of a true contradiction to be -- that is, without playing yet another Nixon
card --, as the rest
of this site aims to show.

And
that comment also applies to any 'dialectically-inspired' responses elicited from those who
might think to question the above
assertions.

Clearly, this doesn't mean that we shouldn't exercise some degree
of sensitivity toward other belief systems (past or present), but we may only do
so in terms of current linguistic protocols. When confronted with what appears to be weird or
paradoxical beliefs, we wouldn't be able to translate or interpret them
literally and claim we understood them. On the other hand, if anyone claimed that
they could do this, it would automatically throw into doubt the validity
of their translation (unless the meaning of the word "translate" itself
had been altered) -- always supposing, of course, that they hadn't merely transliterated
the relevant inscriptions/words
instead.

However, if what had been 'translated' were held to be literally
true, and still remained paradoxical, then whatever else we could make of it, we would have to abandon all talk of its literal truth.
Either that, or, once again, we would have to understand the words "literal" and "truth" non-literally!

[This topic is still under intense debate; on his see Creary and Read
(2000), especially Cerbone (2000). See also
Conant (1991), and Forster (1998).]

So, until and unless DM-theorists explain themselves, we are
forced to conclude that 'dialectical contradictions' fail to depict, or express, anything in
any meaningful sense.

The
above isn't
being asserted because I personally think that reality contains no
contradictions, or because I have concluded that the world either is or is not
as these allegedly 'true contradictions' depict it -- or
even because
contradictions are always false (which is the classical view). To argue along
those lines
would be to fall into the same trap that ensnares DM-theorists, since it would amount
to the derivation of the opposite a priori thesis about reality to that
adopted by DM-theorists, based on an
alternative linguistic convention, which I might in this case have found more acceptable.

On the contrary, contradictions fail to picture
the world not because they are false, but because they aren't pictures to
begin with. They represent the disintegration of the depictive capacity
of language, since
they violate materially-grounded linguistic rules we already have for the use of
the negative particle. [On this, see Essay Twelve
Part One.]

Finally, it could be argued that the above comments are misguided since dialecticians do not question
the general application of principles drawn from FL, such as the
LOC; they merely point
to their limitations when it comes to change. Hence, contradictions
like those illustrated in B1 and B2 are completely irrelevant.

B1:
John Rees wrote and did not write The Algebra of
Revolution.

B2: This four thousand year old inscription says
that its author wrote and did not write it.

So, a critic might object
that since the above do not depict change, reference to them is beside the
point.

Or, so it could be argued.

That particular response will be put under considerable pressure
throughout this and other Essays at this site, where it will be shown that it is
dialecticians who can't actually account
for motion and change, whatever examples are chosen for examination.

"Instead of speaking by the
maxim of Excluded Middle (which is the maxim of abstract understanding) we
should rather say: Everything is opposite.Neither in heaven nor in
Earth, neither in the world of mind nor of nature, is there anywhere such an
abstract 'either-or' as the understanding maintains. Whatever exists is
concrete, with difference and opposition in itself. The finitude of things will
then lie in the want of correspondence between their immediate being, and what
they essentially are. Thus, in inorganic nature, the acid is implicitly at the
same time the base: in other words, its only being consists in its relation to
its other. Hence also the acid is not something that persists quietly in the
contrast: it is always in effort to realise what it potentially is." [Hegel
(1975, p.174;
Essence as Ground of Existence, §119.
Bold emphasis added.]

The answer scientists give
in this case is that elephants do both, they run
and walk. Is this a contradiction? Does this refute the claims made earlier? Can this
anomaly be
'resolved', DM-style by means of (i) a series of a priori, dogmatic assertions
about all of reality for all of time? Or, (ii) by means of disambiguation? Which tactic is going to work?

Well, here is the article's
explanation how this conundrum
was in fact resolved:

"With their awkward, lumbering gait, elephants moving at high speed are not the
most graceful of animals -- but are they walking or running? Now scientists
believe they have an answer: new research confirms that they do both -- at the
same time.

"By observing
elephants moving across a hi-tech track, the team found the hefty creatures run
with their front legs but walk with their back legs. The research
is published in the Journal of Experimental Biology. Earlier
research had suggested that elephants perform a strange, part-walk/part-run
while travelling at speed. But a team
from Belgium, Italy and Thailand was able to investigate this further by using a
specially built track that was able to precisely measure (sic) the forces exerted with
each weighty elephant step.

"Professor
Norman Heglund, an author of the paper from the Catholic University of Louvain,
Belgium, told BBC News: 'We had to build the plates -- you just can't go down to
your local hardware shop and pick up an elephant-sized force plate.' Armed with
these, the researchers headed to the Thai Elephant Conservation Centre to study
the big beasts, which ranged from an 870kg baby to a four tonne adult. The Asian
elephants were encouraged to move across the track, at speed, by their
keepers....

"They
were...filmed using high-speed cameras. By comparing
the measurements from the sensitive force-measuring platform with each frame of
the footage, the scientists were able to look at every tiny movement that the
elephants were making. This enabled
them to calculate the amounts of potential energy (stored energy) and kinetic
energy (the energy that is associated movement), that the creatures were using. Measuring the
relationship between potential and kinetic energy is the key to defining whether
something is walking or running.

"For example,
when walking, as an animal raises its foot from the ground and moves it
forwards, it is converting the stored energy in its muscles and tendons -- the
potential energy -- into kinetic energy. As its foot
lands, the kinetic energy converts back into potential energy, and then back
into kinetic energy as the foot is once again raised, and so on. All the time
the creature is walking, the energy is transferred back and forth between
potential and kinetic energy.

"But while
running, the exchange between potential energy and kinetic energy is continuous
-- rather than one form of energy being recycled into the other, back and forth,
the energy exchange is happening all the time. Professor
Heglund explains: 'The running gait, in most animals, is a bouncing mechanism. In this case,
the potential and kinetic energy are in phase, they both hit a maximum at the
same time and a minimum at the same time, so they cannot be transferred back and
forth.'

"However, the
researchers found that fast-moving elephants seem to both run and walk at the
same time. Professor
Heglund said: 'When an elephant goes at higher and higher speeds, the kinetic
and potential energy shift and start to become more in phase. But when we
looked in detail, we see that the animal appears to be running -- bouncing --
with the front legs, and walking with the back legs. It is as if
he is getting up to a transition speed where he wants to transition from a walk
to a run, but he can't quite do it. It's like he can't quite get up into second
gear.'...

"The scientists
now plan to look at other large animals, such as hippos and rhinos, to find out
if they run or walk. This latest
study confirms the findings of other research, published in the journal
Nature and the Journal of Experimental Biology, that have previously
shown that elephants perform a run-walk hybrid. However, there
are some differences -- while this latest paper suggests the front legs run and
the back legs walk, the other studies suggested the opposite." [Quoted from
here.
Bold emphasis alone added. Several paragraphs merged to save space. Minor typo
corrected.]

So, this apparent
contradiction was resolved by detailed observations (coupled with clear definitions
-- and a modicum of common sense),
which
led to a new discovery: that elephants run with their front legs, but walk with
their back legs (or the other way round!). Had these researchers been dialecticians, it is unlikely that
this advance would have been made; we would merely have been told to "grasp"
this 'contradiction' and move on (no pun intended).

[More on that in Essay Seven
Part One.
Compare this with the
Mickey Mouse Science one finds in books and articles on DM. General logical
issues are discussed in Essay Four; other related topics
-- such as the
"interpenetration of opposites" and change through "internal contradiction"
-- are
reviewed in Essays
Seven Parts One and
Three, as well as Essay Eight
Parts One,
Two and
Three. Those who feel that the
above comments don't in fact address 'dialectical contradictions' (whatever
they are) should read
this,
this,
this, and
this, and then perhaps think
again.]

"If, now, the first
determinations of reflection, namely, identity, difference and opposition, have
been put in the form of a law, still more should the determination into which
they pass as their truth, namely, contradiction, be grasped and enunciated as a
law: everything is inherently contradictory, and in the sense that
this law in contrast to the others expresses rather the truth and the
essential nature of things. The contradiction which makes its appearance in
opposition, is only the developed nothing that is contained in identity and that
appears in the expression that the law of identity says nothing. This
negation further determines itself into difference and opposition, which now is
the posited contradiction.

"But it is one of the
fundamental prejudices of logic as hitherto understood and of ordinary thinking
that contradiction is not so characteristically essential and immanent a
determination as identity; but in fact, if it were a question of grading the two
determinations and they had to be kept separate, then contradiction would have
to be taken as the profounder determination and more characteristic of essence.
For as against contradiction, identity is merely the determination of the simple
immediate, of dead being; but contradiction is the root of all movement and
vitality; it is only in so far as something has a contradiction within it
that it moves, has an urge and activity.

"In the first place,
contradiction is usually kept aloof from things, from the sphere of being and of
truth generally; it is asserted that there is nothing that is contradictory.
Secondly, it is shifted into subjective reflection by which it is first posited
in the process of relating and comparing. But even in this reflection, it does
not really exist, for it is said that the contradictory cannot be
imagined or thought. Whether it occurs in actual things or in
reflective thinking, it ranks in general as a contingency, a kind of abnormality
and a passing paroxysm or sickness....

"Now as regards the assertion that
there is no contradiction, that it does not exist, this statement need not
cause us any concern; an absolute determination of essence must be present in
every experience, in everything actual, as in every notion. We made the same
remark above in connection with the infinite, which is the
contradiction as displayed in the sphere of being. But common experience itself
enunciates it when it says that at least there is a host of
contradictory things, contradictory arrangements, whose contradiction exists not
merely in an external reflection but in themselves. Further, it is not to be
taken merely as an abnormality which occurs only here and there, but is rather
the negative as determined in the sphere of essence, the principle of all
self-movement, which consists solely in an exhibition of it. External,
sensuous movement itself is contradiction's immediate existence. Something
moves, not because at one moment it is here and at another there, but because at
one and the same moment it is here and not here, because in this 'here', it at
once is and is not. The ancient dialecticians must be granted the contradictions
that they pointed out in motion; but it does not follow that therefore there is
no motion, but on the contrary, that motion is existent contradiction
itself.

"Similarly, internal self-movement
proper, instinctive urge in general, (the appetite or nisus of
the monad, the entelechy of absolutely simple essence), is nothing else but the
fact that something is, in one and the same respect, self-contained and
deficient, the negative of itself. Abstract self-identity
has no vitality, but the positive, being in its own self a negativity, goes
outside itself and undergoes alteration. Something is therefore alive
only in so far as it contains contradiction within it, and moreover is this
power to hold and endure the contradiction within it. But if an existent in its
positive determination is at the same time incapable of reaching beyond its
negative determination and holding the one firmly in the other, is incapable of
containing contradiction within it, then it is not the living unity itself, not
ground, but in the contradiction falls to the ground. Speculative thinking
consists solely in the fact that thought holds fast contradiction, and in it,
its own self, but does not allow itself to be dominated by it as in ordinary
thinking, where its determinations are resolved by contradiction only into other
determinations or into nothing

"If the contradiction in
motion, instinctive urge, and the like, is masked for ordinary thinking, in the
simplicity of these determinations, contradiction is, on the other hand,
immediately represented in the determinations of relationship. The most
trivial examples of above and below, right and left, father and son, and so on
ad infinitum, all contain opposition in each term. That is
above, which is not below; 'above' is specifically just this, not to be
'below', and only is, in so far as there is a 'below'; and conversely,
each determination implies its opposite. Father is the other of son, and the son
the other of father, and each only is as this other of the other; and
at the same time, the one determination only is, in relation to the other; their
being is a single subsistence. The father also has an existence of his
own apart from the son-relationship; but then he is not father but simply man;
just as above and below, right and left, are each also a reflection-into-self
and are something apart from their relationship, but then only places in
general. Opposites, therefore, contain contradiction in so far as they are, in
the same respect, negatively related to one another or sublate each other
and are indifferent to one another. Ordinary thinking when it
passes over to the moment of the indifference of the determinations,
forgets their negative unity and so retains them merely as 'differents' in
general, in which determination right is no longer right, nor left left, etc.
But since it has, in fact, right and left before it, these determinations are
before it as self-negating, the one being in the other, and each in this unity
being not self-negating but indifferently for itself.

"Opposites, therefore, contain
contradiction in so far as they are, in the same respect, negatively related to
one another. Ordinary thinking when it passes over to the moment of the
indifference of the determinations, forgets their negative unity and so
retains them merely as 'differents' in general, in which determination right is
no longer right, nor left left, etc. But since it has in fact right and left
before it, these determinations are before it as self-negating, the one being in
the other, and each in this unity being not self-negating but indifferently for
itself." [Hegel (1999),
pp.439-41,
§955-§960.
Bold emphases alone added.]

Detailed comments on the above passage (as it has been
interpreted by a particular DM-theorist, James Lawler) can be accessed here;
several
more will be posted in Essay Twelve Part Five, at a later date.

3.
An alternative translation -- which appears in Volume 25 of Marx and Engels
Collected Works
(MECW) -- renders the last sentence as follows:

"And the continuous origination and
simultaneous solution of this contradiction is precisely what motion is." [MECW,
Volume 25, p.111. This can be accessed
here.]

The above version manages to neutralise some of the criticisms
outlined in the main body of this Essay, but not all. Who, for instance,
"solves" these contradictions, and how exactly do they do it? More pointedly, how do
they manage to do this quite so quickly (i.e., simultaneously
with the "origination" of each new contradiction)? And so many times,
too? [There must be billions of these 'solutions' dotted all along the
trajectory of even the shortest journey.] When this
contradiction is "solved" does this mean that a moving object is no longer in
two places at once, in one of these and not in it at the same time? If not, what
does it mean to 'solve' such a 'contradiction'?

Perhaps even more significant: has a single DM-fan ever
asked these questions, let alone tried to answer them? Or have they become so
theoretically supine that their critical faculties have failed them?

Furthermore, this passage introduces several difficulties of its
own, for it leaves it entirely mysterious from where these contradictions originated. Indeed, it
appears to promote contradictions above motion; they seem to cause it, not it them.

Naturally, in a system
that has descended with modification from AIDS -- where reality is just
the development of Mind -- the ability of 'contradictions' to cause change, or
make things move, seems to make
some sort of crazy sense.

However, as we
discovered in other Essays posted at this site,
dialecticians regularly make this mistake, imagining
that they are talking about the world when in fact they are indirectly drawing
attention to their own idiosyncratic use of language and the implications thereof. That
is, of course, part of the reason why DM is classified at this site as a form of LIE. [For more on this, see Essays
Three Part One
and Twelve
Part One.]

4a. I have just read
Thomas Weston's 'answer' to some of these questions -- Weston (2012).

[I will add a few comments about this in the next
re-write of this Essay.]

5.
To be sure, the overall picture is far more complicated than this opening salvo
might suggest. Later in this Essay, examples will be given where we find that both
stationary and moving objects occupy two places at once. Nevertheless, it is reasonably
clear that Engels didn't have them in mind when he spoke quite so boldly about the
alleged contradictory nature of motion, conclusions supposedly true for all space and time. On the other hand, if he had taken them
into account, his whole 'analysis' would have been completely undermined from
the get-go.

Quantum phenomena
that supposedly violate this caveat (i.e., the claim there is no evidence that
moving objects occupy two places at once, etc.) don't affect this negative conclusion. No one supposes that in
experiments which suggest an electron, for example, can be in two places at once,
that this particle moves from one of these places to the other --
and, indeed, in no time at all. What is supposed
to happen is that when one electron is aimed at a double slit and focused on a
screen, it appears to have taken two separate paths at the same time.
So, it hasn't moved between the latter two trajectories at the same time; it has, it seems,
merely followed two paths. Why DM-supporters view this a confirmation of their
theory, is, therefore, something of a mystery.

It could be argued that the fact one object
can take two paths at once is obviously a contradiction, which shows that nature
is fundamentally contradictory. But, do these two paths 'struggle' with and then
turn into one another (which they should do if
the DM-classics are to be believed)? Do they imply one another so that one
can't exist without the other? If not, then whatever else this
phenomenon illustrates, it can't be a 'dialectical contradiction' -- if,
that is, we are ever told what one of these mysterious
DM-relations or processes actually is.

5a.
However, and independently of the comments made in the main body of this Essay, if
instants have no duration then -- according to
Trotsky -- they don't, or can't, exist,
since they are merely 'abstractions'.But,
exactly what they have been 'abstracted' from, or what they are predicated
upon, Trotsky forgot to say. How does one abstract an instant?
Indeed, insubstantial spectres such as these can't be what all temporal intervals have in
common: non-existent duration-less 'points'? Is this what duration
is composed of? A set of 'instants' that not only have no duration, but
don't actually
exist? [On this, see Note 6.]

6.
'Abstraction' is critically dissected in Essay Three
Parts One and
Two.

Instants in time share nothing with our experience of time, and so they can't
be derived from it by a 'process of abstraction'. Moreover, attributing such
durationless points to "moments in time" would be to assign them properties they
don't have -- namely, non-existence! Ordinarily, we associate a "moment
in time" with a few seconds (depending on context). If someone were to say "Wait
a moment!", and such a moment were durationless, that would be tantamount to
saying "Don't wait at all"! The phrase "a couple of moments" would be the
equivalent of "no moments whatsoever".

Of course, it could be argued that scientists and philosophers
extrapolate from finite moments in time (i.e., from finite time intervals)
to such
instants all the time (no pun intended). Hence, as such, these instants are Ideal constructs, capable of
being mapped onto, or by, the
Real Numbers.
That argument/analogy has been neutralised
here (and, in general, in
the two Essays linked to above).

7.
This idea might proceed as follows: If
knowledge results from the reflection in the mind of
the complexities
found in reality (mediated by practical activity) -- which is
"relative" and hence correct only "within certain
limits" -- then, even a provisionally correct theory must faithfully
represent the contradictory nature of the world. In this limited sense,
human, or social, categories would be relatively adequate to the world (again,
if they are correct, and have been tested in practice), but they won't have been projected,or imposed, onto it. This
interpretation might then allow DM-theorists to draw substantive conclusions
about the world from a consideration, or application, of the concepts and
categories found in
thought (howsoever they got there). Even so, such theories would still only approach absolute truth asymptotically.
[Indeed, some might want to call concepts and categories like this, "presuppositions".
This approach has even been given the grandiloquent title "Descriptive
Metaphysics" by some
Analytic Philosophers -- or, to be more accurate, by
Peter
Strawson (Strawson (1959) -- on that, see
here.]

[If, on the other hand, the Kantian
or Hegelian route is taken by dialecticians, whereby
the concepts and categories of thought are what they are because of the nature
of cognition, or of 'dialectical reason' itself, then they should be honest, and admit that they
have indeed imposed
their ideas on nature, contrary to what they
swear they never do. To
date, only certain
HCDs seem prepared to take that detour.]

Of
course, this flies in the face of Novack's point:

"A consistent materialism cannot proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphases added.]

Be this as it may, such claims
have been examined
in greater detail
here and
here.

In addition
to the above, it is worth highlighting several serious problems this approach to
knowledge brings in its train:

(1) Elsewhere, it will be argued that this way of looking at language forms part
of what I have called the RRT, which is a theory that actually projects 'knowledge'
onto nature
under the pretence that language/'cognition' merely
reflects what is already there.

[RRT = Reverse Reflection Theory; this will be
explained in more detail Essay Twelve Part Four.]

Because of their implicit acceptance of the RRT dialecticians assume that they are in a position to state
in advance of experience what the
world must be like beforeanyone knows what it is like.
This
involves them in specifying what it is that certain
'concepts'/words
correspond with in realitysolely on the basis of the supposed logico-linguistic features of the
mode of expression in which
they are expressed (i.e., the 'concepts' and the language used to that end).

[They certainly wouldn't want to
characterise the above approach this way, nor would
they even recognise that this is what they actually do. However, scores of examples were given in Essay
Two that show that all
-- i.e., 100% of --
dialecticians appear to have what can only be described as a neurotic tendency
to assert dogmatic and a priori theses about fundamental aspects of
reality, true for all of space and time, based on the
supposed meaning of a handful of words, or 'concepts', virtually all of which
have been imported from Hegel, other mystics, and
Traditional Thought. (A detailed analysis of the class-compromised
origin of core DM-theses can be accessed
here and here.)]

Of course, this DM-thesis (i.e., that language reflects the
world) can't itself have been derived from the world. [Or, if it can,
we have yet to see the proof.] In that case, this theory -- which claims that knowledge is a
complex 'reflection of reality' -- must itself have been imposed on nature
(once more, contrary to the claim that
this is never done).

Nevertheless, an additional motivating idea operating behind the scenes here seems to be that
reference to
experience, observation or practice is necessary if we are to weed out certain items
that aren't actually found in nature, or
which do not reflect 'objective' reality. Otherwise, of course, an
appeal to empirical checks
and practice
in order to test which linguistic expressions are genuinely 'represented' in nature by real
material processes or relations -- or, indeed, which referred to them -- would be an empty gesture. In fact, because
it is impossible to specify ahead of time which parts of this (now
supposedly
legitimate) a
priori DM-picture of the world might never be eliminated after testing
in this manner, all knowledge
is deemed provisional.

Or, so it could be, and has been, argued.

Despite
this, DM-theorists still aim to tell their readers what the fundamental aspects of
reality are, valid for all of space and time. They inform us that
everything in reality is contradictory and constantly changing, that
all objects and processes are powered by, and change because of, the interplay between 'interpenetrated, internal opposites',
and that the world is a single interconnected
'Totality'
composed of 'mediated' parts/wholes,
governed by the laws of dialectics, which is susceptible to 'rational' explanation. In
addition, we are informed
that each part is dependent on every other part, and that the nature of the
whole is determined by the complex interconnections between the parts, etc., etc.

But, the only 'evidence' 'substantiating' universal
theses like this is, it seems, a series of inappropriate extrapolations from a few
heavily
doctored linguistic expressions -- indeed, as we will see as this Essay proceeds
--, which are then 'justified' by an appeal to a series of highly dubious,
but nonetheless
seriously garbled examples, that utilise what can only be called, Sub-Aristotelian Logic,
supported by a handful of highly clichéd,
specially-selected, constantly recycled,
contentious examples. [In fact,
I call
this Dialectical Dog's Dinner, Mickey Mouse Science,
in Essay Seven Part One.]

Unfortunately, this means that if we
were
looking for a theory that was capable of explaining, or helping us understand,
nature, DM would fail to make the bottom of the reserve list of viable
candidates.

Be this as it may, if
nature were reflected in thought, so that
aspects of reality were embodied in language, and if it were then claimed that this justified inferences
from language to the world, it would be impossible
to account for falsehood. If thought is indeed a
reflection of the world, then it could never be
incorrect -- in the same way that a mirror image or reflection is never wrong.

Of course, it could be argued that a sophisticated application of
the RTK (not to be confused with the
RRT), with its
emphasis on the 'partial' or 'relative' status of truth, on practice and the
"one-sided" nature of abstractions (etc., etc.), is able to neutralise these
difficulties. After all, mirrors can and do distort reality (at least with
respect to left-right symmetry, or an object's morphology (in, say, a
hall of
mirrors), etc.), but few are
taken in by this. Moreover, it could be maintained that when other criteria are
incorporated into the mix (such as increased consistency and greater explanatory
power), defective theories could be weeded out as part of the search for an ever more accurate
account of the world --, and, of course, how to change it.

[RTK = Reflection Theory of Knowledge.]

Maybe so, but mirrors can't reflect what isn't there.
Hence, if language and thought were mirrors (or even lenses, to vary the
metaphor) -- distorting or otherwise -- we
would have to conclude that everything expressible in language must exist
in reality. Even though they might distort things, mirrors can't conjure into existence objects and processes that
aren't there. But -- disciples of
Meinong
excepted --, who in their left mind is prepared to admit that whatever language contains must exist,
or subsist,
somewhere in nature?
Who wants to allow for the existence of, say,
Harpies and
Gorgons -- even in a
distorted form -- simply because we have words for them? On the
other hand, if it were possible to include such 'entities' so easily into 'Being' (by the
expedient of simply naming
them), why bother looking for evidence in support? In fact, if this approach to
knowledge were viable, any search that went
beyond leafing through every Dictionary,
Thesaurus,
Encyclopaedia of Mythology, and Textbook of Grammar on the planet would be
superfluous. In that case, Science would become a sub-branch of Lexicography,
or, indeed,
Hermeneutics.

It could be argued that even mythical beasts and
fictional characters are composed of 'images' that have been derived from
experience. This is where human judgment can go wrong: it knits together some of these
elements in incorrect or fanciful ways.

Figure Two: A 'Dialectical'
Harpy?

For example, a Harpy is formed from a
combination of human and animal 'images', but experience tells us that
these beasts don't exist. Hence, while we can certainly imagine all sorts of 'possible beasts'
or 'objects', only some of them actually exist (as far as we know).

This particular
response will be
tackled in Essay Three Part Five, and Essay Thirteen Part One (here).
Suffice it to say that (a) The idea under review here is that it is words, not
'images', that reflect reality. In that case, this metaphor is committed to the
view that if we have words for something, it must exist, and (b) If we are to
rely on 'images' then we would be
stuck in a
solipsistic universe. ['Images' are examined in detail in Essay Thirteen
Part One.]

Of
course, anyone committed to such a theory (i.e., that which was alluded to in
(a) above) would have problems pointing out the ontological equivalent of
prepositions, conjunctions, adverbs, definite or indefinite articles, and the
like -- that is, precisely what it is in the world they 'reflect.

It
might be wondered why anyone committed to the above view of images (i.e., the
allegation presented in (b) above) would in effect be trapping themselves in a
"solipsistic world". The answer is quite simple: they would have no way of checking
the 'veracity' of their images except by checking them against yet more images.
Practice would be no use here, since all that such an individual would have
access to would be images of practice. Nor would it do to appeal to
'commonsense', or to the "naive beliefs of ordinary people" (as
Lenin
attempted to do), and that is because all that such an individual would have
would be images of 'commonsense', and images of ordinary folk and their
beliefs. That is why it was asserted above: "they would have no way of checking the
'veracity' of their images except by checking them against yet more images."
In short, they would be trapped in a world composed of their own 'subjective' images -- a
solipsistic world. [This is a greatly shortened version of a much longer and
more detailed argument set-out in full in Essay Thirteen
Part One.]

Putting
even this worry to one side, it might be
difficult, too, for anyone who accepts this view of language (i.e., that which
was alluded to in (a) above, again) to explain how
words for non-existent beings (such as Harpies and Gorgons) -- even if these are based on
'images' stored in each individual dialectical head -- can be harmonised with a social
interpretation of language.

However, the specific point under consideration here was in fact
the following counter-response:

[That the aforementioned]
interpretation might then allow DM-theorists to draw substantive conclusions
about the world from a consideration, or application, of the concepts and
categories found in thought (howsoever they got there).
Even so, these theories would still only approach absolute truth asymptotically.

Now, we have already established that DM-theorists
go way beyond seemingly modest disavowals
like this, claiming to know what the fundamental features of
reality are -- valid for all of space and time --, but, derived solely from the alleged meanings of certain words.

Some
might think to bring in ideology here, but that can't affect the above comments.
Ideology supposedly 'inverts' things. Even if this were an apt metaphor,
ideology can't create (merely by inversion or reflection)
what isn't there. [Of course, this metaphor might not be apt. I will say
more about that in Essay Three Parts Four
and Five.
Until then, see here.]

Moreover, an earlier reference to the hermeneutic
gyrations required to make this theory work was deliberate. The latter word in
italics is in fact derived from the Greek 'deity', Hermes, the interpreter of
the 'Gods'. That term was pointedly chosen because of the many accusations advanced at
this site that DM is
just a contemporary version of Hermeticism
-- minus the overt theology.

This allegation is also linked to another ancient idea that
Philosophy and Theology were invented by
Hermes (or, in Egypt, by
'his' equivalent,
Thoth -- on
this see Boylan (1999), Faivre (1995), and Fowden (1993)). Of course, Philosophy
as a discipline was invented by ruling-class theorists, but it was also an
important and integral aspect
of an ideological package aimed at tracing the supposed source of ruling-class ideology back to the thoughts of the 'gods'
themselves. [Why this is so will be
explored in Essay Twelve Parts Two and Three (summary
here),
where the phrase "ruling-class theorist" will be explained more fully. Until
then, see here,
here,
here
and here.]

Furthermore, this isn't as wild an accusation as might at first seem. In fact,
it was derived from Marx himself:

"Feuerbach's
great achievement is.... The proof that philosophy is nothing else but
religion rendered into thought and expounded by thought, i.e., another form
and manner of existence of the estrangement of the essence of man; hence equally
to be condemned...." [Marx
(1975b), p.381. I have used the on-line version, here. Bold emphasis
and link added.]

[Indeed, it is arguable that this is part of the reason why Marx
had abandoned
Philosophy by the mid-, to late-1840s; on that, see
here.]

This
ancient approach to
knowledge -- which has, in one form or another, dominated much of 'Western' (and
'Eastern') thought
ever since -- sought to connect
obscure philosophical jargon with the divine, 'rational', a priori, structure of
reality (i.e., with 'Being Itself').

It is
this
observation that partially motivates the claim advanced in these Essays that Traditional
Thought
represents, or is an 'image' of,
not the material world, but an ancient ruling-class view of
an Ideal World; a world that supposedly 'exists' anterior to experience, which is more real that the universe we see around us. Boss-class theorists
further inform us that this hidden world
-- accessible to thought alone -- underlies 'appearances',
and
lends to reality its 'essence'. That world is therefore thoroughly immaterial.

Given the
traditional approach to knowledge, it is the language used by its
theorists that tells them what this hidden world must be like
-- for they have no
other access to it. In that case, this hidden world is a reflection of
specific forms-of-thought/language --, not the other way round. [As noted earlier, I
call this the RRT,
and a sub-branch of
LIE.
More about that in Essay
Twelve Part Four, when it is published.]

In each Mode of Production, different
versions of the same general belief (in the divine, or a priori, structure of
reality) have been utilised by Traditional Thinkers to rationalise the wealth
and power of contemporaneous elites, and thus the different
relations of production that dominated human beings in each such mode. It isprecisely
here -- where dialecticians have accepted, appropriated and imported into
Dialectical Marxism significant segments of this ancient world-view -- that ruling ideas
have succeeded in ruling militant
minds.

Some might object that philosophical ideas can't have remained the
same for thousands of years, across different Modes of Production; that idea runs
counter to core ideas in Historical Materialism.

But, we don't argue the same
for religious belief. Marx put no time stamp on the following, for
example:

"The foundation of irreligious criticism is:
Man makes religion, religion does not make man. Religion is, indeed, the
self-consciousness and self-esteem of man who has either not yet won through to
himself, or has already lost himself again. But man is no abstract
being squatting outside the world. Man is the world of man -- state,
society. This state and this society produce religion, which is an inverted
consciousness of the world, because they are an inverted world.
Religion is the general theory of this world, its encyclopaedic compendium, its
logic in popular form, its spiritual point d'honneur, its enthusiasm, its
moral sanction, its solemn complement, and its universal basis of consolation
and justification. It is the fantastic realization of the human essence
since the human essence has not acquired any true reality. The struggle
against religion is, therefore, indirectly the struggle against that world
whose spiritual aroma is religion.

"Religious
suffering is, at one and the same time, the expression of real suffering
and a protest against real suffering. Religion is the sigh of the
oppressed creature, the heart of a heartless world, and the soul of soulless
conditions. It is the opium of the people.

"The abolition of religion as the illusory
happiness of the people is the demand for their real happiness. To call
on them to give up their illusions about their condition is to call on them to
give up a condition that requires illusions. The criticism of religion
is, therefore, in embryo, the criticism of that vale of tears of which
religion is the halo." [Marx
(1975c),
p.244.
Italic emphases in the original.]

The above remarks applied back in Babylon and
the Egypt of the Pharaohs,
just as they did in Ancient China and the rest of Asia, The Americas, Greece,
Rome and throughout Europe, Africa, Australasia, as they have done right across the planet ever since.

The same is true of the core thought-forms of Traditional
Philosophy -- that there is indeed this 'invisible world', accessible to thought
alone --, especially since Marx, as we have seen, also argued that:

"...philosophy is nothing else but
religion rendered into thought and expounded by thought, i.e., another form
and manner of existence of the estrangement of the essence of man; hence equally
to be condemned...." [Marx
(1975b), p.381.]

[This topic
will be discussed in more detail in Essay Fourteen Part
One (summary here);
the pernicious effect it has had on Dialectical Marxism has been exposed
here.]

Naturally, the (postulated!) DM-account of the origin of mythical beings is
more sophisticated than previous paragraphs might suggest. But, a
distorted view of reality, howsoever it is produced -- whether or
not it is a result of alienation, or based on a "one-sided" theory, or ideology,
or, indeed, is a spin-off from the process of abstraction itself,
even if it results in an upside down image, a blurred one, or even one wearing a
pink tutu -- it matters not; it is still a view of reality (given
the applicability of the reflection metaphor, sophisticated version
or otherwise), and in that case it is an Ideal view. A mirror can't invent.
Hence, this metaphor implies that things like
dragons, fairies, ghosts and hobgoblins -- not to mention
Atlantis,
heaven, hell and Nowhere -- must exist somewhere, in some form, just because we have the words for them!

On the other hand, if these 'entities'
don't exist,
then the mirror metaphor is radically defective and should be abandoned.

[DL = Dialectical Logic.]

Of course, it could be objected that raising superficial
objections like those above, based on contingent features of mirrors, or even the
world, entirely misses the
point; dialecticians are interested in the essential nature of reality, and
these are reflected in (or by) DL.

Nevertheless, more-or-less the same objections can also be ranged against the principles
supposedly encapsulated by DL.
But worse, as
we have seen(here,
here,
here,
here and
here), DL is far too confused to
have 'captured' anything in thought, distorted or otherwise.

Or, to put the same point in reverse: if the essential
nature of reality is reflected in (or by) DL, then reality would be a madhouse.

Figure Three: What The World Might Look Like

If
DL Were An Accurate Reflection Of It

Furthermore, since these general/'essential' features of reality are often
highly abstract (or they are expressed in suitably abstract language), the contention
advanced here (that these are the product of misconstrued rules of grammar,
and aren't truths in any shape or form) has more than just a little prima facie plausibility
going for it.

[Incidentally, the above comments can also
count as an answer to the objection that the a
priori concepts and categories of DL capture the form but not the content of
reality. Again, since this topic is examined in more detail in Essay Three
Part One and Essay Twelve, no more will be
said about it here.]

(2) The phrases "relative adequacy" and "relative truth" are
no less hopelessly unclear. Expressions like these are obviously linked to the DM-thesis that
human knowledge "asymptotically" approaches 'absolute
truth', over time, which implies that at any point it is incomplete, or even
radically incomplete. However, when examined more closely, these ideas areinimical to DM. That is because they imply humanity is and always will be infinitely ignorant
of everything, no matter how "relatively" complete our knowledge of anything
might seem to be at any given point in history. On that basis, far from being "relatively adequate", or even "relatively true",
knowledge will always remain infinitely far from the truth, and hence would possess
an infinitely high probability of being false. That in turn is because the difference between a
finite and an infinite body of knowledge is itself infinite.

A relevant passage from Engels comes to mind again (which was
commented on in Essay Two):

"The identity of thinking and being, to use
Hegelian language, everywhere coincides with your example of the circle and the
polygon. Or the two of them, the concept of a thing and its reality, run side by
side like two asymptotes, always approaching each other but never meeting. This
difference between the two is the very difference which prevents the concept
from being directly and immediately reality and reality from being immediately
its own concept. Because a concept has the essential nature of the concept and
does not therefore prima facie directly coincide with reality, from which
it had to be abstracted in the first place, it is nevertheless more than a
fiction, unless you declare that all the results of thought are fictions because
reality corresponds to them only very circuitously, and even then approaching it
only asymptotically…. In other words, the unity of concept and phenomenon
manifests itself as an essentially infinite process, and that is what it is, in
this case as in all others." [Engels to Schmidt (12/03/1895), in Marx and Engels
(1975), pp.457-58.]

First
of all Engels failed to say how he knew it was true that knowledge is
convergent. Of course, if what Engels actually said were true, it would be
infinitely wrong, or, as noted above, it would possess an infinitely
high probability of being false. That is because, when asserted, that claim must itself be
infinitely far from the 'truth', if we are to believe what Engels says in
the above passage. And, manifestly, the fact that
knowledge is an infinitary process can't be confirmed in practice (or,
indeed, in
any other way).

Secondly,
the idea of an asymptotic approach in mathematics is
connected with the concept of a limit -- if the limit concerned can be shownto exist. Alas, Engels failed to
prove that there is such a limit for knowledge to approach in the
required manner (in fact, he didn't even so much as attempt such a proof;
and, as far as can be ascertained, no dialectician since has bothered to
fill in the details, either -- or shown they are even aware of the problem!). In that case,
Engels's 'mathematical metaphor' is doubly inappropriate: if there is no limit,
human knowledge must be divergent. And, if that
is so, then at any point in human history, our knowledge must be infinitely far
from
'Epistemological Valhalla'
-- which, it is worth recalling, still hasn't been shown to exist. On
this view, given Engels's inapt metaphor, humanity will always be infinitely
ignorant of anything and everything!

Of course, it could be argued that just because certain
iterative functions in
mathematics yield infinite sequences that doesn't mean that the
distance between any intermediate value given by a partial sum of that
function and the point toward which it is converging is itself infinite. For
example, the sequence: 1 +
1/2 + 1/4 + 1/8 +...+ 1/2nconverges on 2 (as n→+∞), but none of the
rational
numbers (formed from the partial sums of this series)
is infinitely far from 2.

This isn't strictly true
(since the (mathematical) distance between any two rational numbers is itself
infinite), but even if it were correct, the above would
have been an effective response had
Engels bothered to prove that the limit he claims exists (implied by the asymptote
metaphor) actually does exist. But since he didn't, it isn't.

The only way the above sceptical conclusions can be
neutralised
would involve a denial that 'absolute knowledge' is in any
way infinitary. Clearly, that would place a condition on the object of
knowledge before we knew what it was! Of course, it would also mean that several
passages from the DM-classics (quoted
elsewhere at this site)
should
be revised -- or ignored --, along with the above 'asymptote' metaphor, since they
manifestly do imply such an infinitary task. Indeed, they go further -- they say
it is infinite, and even call it a "demand".

7a. That is to say, our
everyday -- or even our scientific -- thoughts about motion aren't
contradictory, whereas those concocted by Idealist Philosophers might be
-- that
is, if
any
sense can be made of what they actually said about it!

8.
As noted above, in Hegel's system, the existence of 'real contradictions' made
some sort of crazy sense. Hence, if reality is just "THOUGHT" writ large, then linguistic categories
may be projected ("foisted")
on
reality quite 'legitimately', since nature is 'self-developing Mind' anyway --, or,
at least, it is an aspect of it. But, as we will see in Essay Twelve, this doctrine
was itself a throwback to
Ancient Greek (and
earlier) religious ideas, where conflicts in nature and society were depicted in
mythical,
anthropomorphic, and theological terms (i.e.,
where it was thought that the universe was the playground of evil or
benevolent agents/'gods') -- later translated into in ethical, political, conceptual
and purely
abstract linguistic forms, after philosophical speculation had kicked in (as
Professor Havelock noted).

[The
reason why this ancient view of the world was conducive to wider ruling-class interests
will also be outlined in Essay
Twelve(summary
here) -- but it was hinted at in
Note 7. (Also see:
here
and here.)]

8a.
Of course, it could be argued that since
everything in the universe is in motion, the question, "Which came first, motion
or contradictions?" doesn't arise. However, as we will
see, things aren't
quite so straight-forward. Quite the reverse, in fact. [No pun intended.]

9.
Quotations from Lenin (and others) concerning 'internal contradictions' and
self-development (etc.) were posted in Essay Two.
Cf., Rees (1998), p.7. This topic is
examined in much more detail in Essay Eight Parts
One and
Two.

9a.
Although Woods and
Grant came very close to asserting this (i.e., that there is an 'internal motor' in
moving objects that makes keeps them moving):

"So fundamental is this idea to dialectics that
Marx and Engels considered motion to be the most basic characteristic of
matter.... [Referring to a quote from Aristotle:] [T]his is not the
mechanical conception of motion as something imparted to an inert mass by an
external 'force' but an entirely different notion of matter as self-moving....

"The essential point of dialectical thought is not that it is based on the idea
of change and motion but that it views motion and change as phenomena based on
contradiction.... Contradiction is an essential feature of all being. It lies at
the heart of matter itself. It is the source of all motion, change, life and
development. The dialectical law which expresses this idea is the unity and
interpenetration of opposites....

"The universal phenomena of the unity of opposites is, in reality, the
motor-force of all motion and development in nature. It is the reason why it is
not necessary to introduce the concept of external impulse to explain movement
and change -- the fundamental weakness of all mechanistic theories. Movement,
which itself involves a contradiction, is only possible as a result of the
conflicting tendencies and inner tensions which lie at the heart of all forms of
matter....

The long quotation from Hegel, given
above, shows where these two
'discovered'
these odd ideas -- they certainly didn't obtain them from any scientists
living on
this planet (not already in thrall to such odd ideas). [On this, see Essay Eight Part
One.]

10.In
fact, Engels himself torpedoed the idea that forces can be viewed as
'contradictory opposites' when he claimed that:

"All motion is bound up with some change of place…. The whole of
nature accessible to us forms a system, an interconnected totality of bodies….
[These] react one on another, and it is precisely this mutual reaction that
constitutes motion…. When two bodies act on each other…they either attract each
other or they repel each other…in short, the old polar opposites of
attraction and repulsion…. It is expressly to be noted that
attraction and repulsion are not regarded here as so-called 'forces', but
as simple forms of motion." [Engels (1954),
pp.70-71. Bold emphasis added.]

As will be
argued in detail in Essay Eight Part
Two, this observation pulls the rug from under anyone
who (i) wants to maintain that forces can be used to model contradictions, and
(ii) views Engels as some sort of authority in such matters.

Anyway, and despite the above, this DM-account of motion does no real work; the
explanation of movement isn't advanced one nanometre by re-describing
it as "contradictory". The supposed 'contradiction' in motion (where a body both
is and is not, etc., etc.) neither initiates, changes, nor sustains movement.

Furthermore, if Absolute Space is left out of the picture, the
precise nature of motion clearly depends on the
inertial frame
chosen. It doesn't
depend on the simultaneous non-occupancy and occupancy of point locations. This
can be seen from the fact that given a particular frame of reference, a body
could be at rest relative to that frame, but with respect to another frame
it could be in motion. Hence, motion is inertial-frame-sensitive, not
'vaguely-located-point-occupancy-and-non-occupancy'-dependent.

It would seem, therefore, that unless
DM-theorists believe in Absolute Space, their insistence that motion is
contradictory (because of their quirky view of such two-point occupancy at the
'same moment') is unsustainable.
Relative notions of space imply that the 'contradictory' behaviour of moving
bodies (if such it be) is a consequence of a change of reference frame: in that
case, bodies are in motion -- or they are stationary -- depending on
which inertial frame is selected. But they wouldn't be either
motionless or moving because of the alleged contradictions inherent in
motion itself. In which case, the 'contradictory' nature of motion can't be an
'objective' feature of reality if it promptly disappears as soon
as a different inertial frame was selected.

It
could be argued that just because motion apparently stops and starts according
to the choice of reference frame no more means
its contradictory nature wasn't objective than it would mean that, say, the boiling point of water wasn't really 100ºC if it were measured in
degrees Fahrenheit or in degrees
Kelvin.

Unfortunately, if that constitutes an effective reply to the points made
above, it would at the same time prove fatal
to the DM-view of motion. That is because it openly concedes that scientific
knowledge is conventional.

Again, exception could be taken to that response. It could
be argued that the fact that the temperature of a body can be read on two or
more different conventionalised scales doesn't imply that temperature itself (or whatever it
supervenes upon)
isn't an objective feature of
reality. The same goes for the
depiction of motion in different reference frames.

However, these two cases aren't analogous; no matter what system we use, a body has some temperature or
other (with the latter defined perhaps in terms of
its
energetics).
This isn't the case with motion and the choice of inertial frame (unless,
of course, we count a zero
velocity as a velocity by default -- but, even then, the alleged 'contradiction'
would still vanish).

In one particular frame, a body
could be in motion and (assuming DM is correct) appear to be 'objectively' contradictory. In
another frame, and at the same time, that body could be stationary and
objectively non-'contradictory' (in Engels's sense), too. Hence, at the
same time, a body could be moving and not moving, 'contradictory' and 'not
contradictory'. Which of these options is finally settled upon will be a
consequence, not of the nature 'motion itself' (whatever that is), but of the choice of reference frame. Since reference
frames aren't 'objective' features of the world (they are human inventions!),
and since the 'contradictory' nature of motion is sensitive to choice of frame,
the conclusion seems inescapable: the 'contradictory' nature of motion (if
such it be) isn't an
'objective' feature of reality, either.

Alert dialecticians at this point might want to argue that this
sentence is eminently contradictory:

"Hence, at the
same time, a body could be moving and not moving, 'contradictory' and 'not
contradictory'."

But, this is just another ambiguous sentence, and its allegedly
contradictory nature will disappear upon disambiguation, as we saw, for example,
here.

It could be argued that the above would mean that motionitself isn't an objective feature of reality if it disappears in the
above fashion when a different reference frame is chosen. But, that isn't so, for if an object is
moving with reference to one frame, but is stationary with respect to a second
frame, then other objects will thereby be moving in a different way
with respect to that frame. So, while the alleged contradiction would disappear
inside the frame in question,
motion in the wider system wouldn't. For example, if the first reference frame
is a volume interval containing only, say, the Moon, and that frame is stationary, the Earth will be in motion
relative to that frame even while the
Moon isn't. Swap the reference frame to a volume interval that contains
only the Earth, mutatis
mutandis, and the Moon will now be moving relative to a stationary
Earth.

[Sure, the Earth will still be rotating, but all we have to do is
make the reference frame a finite region on the Earth's surface, and the Earth
would stop rotating relative to this new frame. For example, from where you are
now sat, or stood, the earth appears not to be rotating, which used to be one of
the strongest arguments that the earth is in fact stationary. (On whether or not the
earth is 'objectively' in motion, see
here.)]

This means that relative motion (at least as it is viewed in modern Physics) is a
conventionalised bi-product of the choice of inertial frame. Therefore, if
DM-theorists are to rescue the 'objectivity' of their theory from the trashcan
of 'subjectivity', it looks like they will have to postulate the existence of Absolute Space. Otherwise, they
will have
to concede that the 'contradictions' they attribute to motion are in fact
artefacts of the choice of reference frame, and not something inherent
in moving bodies.

It isn't easy to see a way out of
this DM-cul-de-sac -- or at least one that makes no further
concessions to conventionalism -- or, indeed, one that makes unwelcome concessions
to
Space/Time Absolutism.

This partly explains why (a few generations
ago), in Stalinist Russia, philosophers and scientists found it difficult to
square Einstein's theory with DM, and hence why some rejected the TOR. If revolutionaries are still unaware of these problems,
STDs a few generations ago certainly weren't. [Cf., Graham
(1971), pp.111-38; see also Joravsky (1961), Krementsov (1997), Vucinich (1980,
2001), and Wetter (1958).]

[STD = Stalinist Dialectician; TOR = Theory of
Relativity.]

Once more, it could be objected that even if the above were
correct,
once moving (in a suitable inertial frame), an object will be doing something
contradictory.

My reply to that
rejoinder will occupy the rest of
this Essay.

11.
This isn't meant to single Engels out here for special attention; it is equally
impossible to determine what, if anything,
Zeno, Hegel
or Lenin were trying to tell us about motion.

However, if it is maintained that systems of supposedly contradictory
forces are responsible for the contradictory nature of motion, then it would be difficult to account for un-accelerated
motion. Clearly, this sort of change takes place where no net forces are
operating. That being so, the exact source of the alleged contradictions here
would be
even more obscure.

Of course, one consequence of DM seems to be that there might
be no un-accelerated motion in nature -- in that (i) The opposite supposition would involve a body
possessing identically the same velocity from moment to moment -- which
would, of course, amount to a fatal concession to the LOI; or that (ii) It
wouldn't be moving in a gravitational field, which, in this universe, is
impossible. Nevertheless,
DM-inspired conundrums like this will not, I take it, worry genuine scientists
too much, or for very long.

[LOI = Law of Identity.]

And all this
is, of course, quite apart from the fact that such a DM-view of velocity (if
such it may be called) will
have to be imposed on nature.

As far as (ii) is concerned, given the
additional fact that
gravitational forces have been
edited out
of the picture in Relativity Theory (on that, see
here), even
if this were so, an appeal to such forces to account for acceleration would be
to no avail, since there are none!

Moreover, in relation to (i), if a suitable frame of reference is chosen, any
body can be said to have zero velocity and be undergoing acceleration for about as long as it takes hard-core DM-fans to
abandon their criticisms of the LOI.

Hence, for any body, b, moving at v
kmph relative to the centre of mass of the Galaxy, say, let a reference frame for it
also move at v kmph with respect to that centre of mass. In that
case, b will have zero velocity with respect to that frame. The only
response a DM-acolyte could make to this would, it seems, have to involve a
reference to 'abstractions' (i.e., in that this involves the use of "abstract
identity"). That last ditch, desperate DM-defence will also be examined, and demolished, in Essay
Six.

11a.
Hegel's
'analysis' of Identity was partially covered
here, and again indirectly throughout Essay Six;
it will be
examined more fully in Essay Twelve (summary
here).

11b. That is because,
if it is unclear what is being proposed -- as is the case with L9, given the
convention introduced in L7 -- then nothing has yet been proposed.

L9: B is at
(X1, Y1, Z1),
at t1 and not at
(X1, Y1, Z1),
at t1, and B is at
(X2, Y2, Z2),
at t1.

L7:
(X1, Y1, Z1) is
not the same place as
(X2, Y2, Z2).

Of course, if L9 depicts one of the ambiguous cases mentioned
already (that is, if B is in fact stationary -- like the car which was half in,
half out of that garage), then it will be clear what is being proposed.
But, in that case, L9 won't provide us with the required necessary and
sufficient conditions for movement, and we would be right back at square one again.

Anyway, in order to
see if some sense can be made of what Engels was trying to tell us, I have
ignored this serious difficulty for the present. However, I will return to it later since it will soon become
apparent that his theory can only be made to work if we ignore the ordinary
use of language and substitute for it distorted 'philosophical' jargon --, as both Marx and Engels
pointed out:

"The philosophers have only
to dissolve their language into the ordinary language, from which it is
abstracted, in order to recognise it, as the distorted language of the actual
world, and to realise that neither thoughts nor language in themselves form a
realm of their own, that they are only manifestations of actual life."
[Marx
and Engels (1970), p.118. Bold emphases added.]

Engels clearly forgot about his earlier warning when he began
importing Hegelian gobbledygook into Marxism!

This isn't either a minor or a trifling point; it is in fact central to understanding
why Traditional Philosophers and dialecticians find they have to impose
their theories on the world, and why their ideas invariably collapse into
LIE. [On this, see
Essay Twelve Part One and Essay
Two.]

12.
A detailed discussion of these aspects of Zeno's analysis of motion can be found in Angel (2002). Also,
see Note 19a and Note 24,
below.

[Incidentally, this way of looking at the
Reals is outlined in Newton-Smith (1980).
On whether time is composed of 'instants', see Read (2007), pp.79-115.]

12a. But
Trotsky
wasn't, of course, the only one to ignore this distinction. Engels also failed to
consider the possibility that an object could be in two times for the same
place -- i.e., in and not in one instant, at that place. But, if time
advances while bodies move (or indeed stay still), and everything is contradictory, then this must surely be
possible.
And if that is so, what is to stop us saying that a moving body occupies
the first place in one of these 'odd instants', and the next place in the second
overlapping instant -- locating the alleged contradiction in time, and not in
space or motion (or, perhaps, even eliminating both if we juggle around with
these options until we get the 'right' result)?

Of course, it could be pointed out that if a body
is
in two times for the same
place then it must be stationary.

In
order to neutralise that objection it might be wise to examine the subtle
differences that exist between these two sentences (always assuming there are any):

B1: Body b is in two different times for
the same place.

B2: Body b is in the same place at two
different times.

I
don't propose to do that here, but it is worth noting that
neither of these imply that the said object is stationary, since that object
could still be moving and could return to the original location at a later time --,
hence, a moving object could be in the same place at two different times.

13. This
is taken to be an important DM-assumption since it is the only way that Engels's
claims about the contradictory nature of motion can be defended, as argued at
length in the main body of this Essay.

14.
It is worth pointing out that L13 doesn't say that b is both at p1 and
not at p1 at t. What it
does say is this:

L13: For some b, for just one instant t, for
three places p1, p2 and p3,
b is at p1 at t, but not at p2
at t, and b is at p3 at t, where p2
and p3 are proper parts of p1.

Hence, a finer-grained analysis of position allows for the
fact that, while at the macro-level an object might be locatable in one
place (say, p1) at one
'instant', at the micro-level it could still be in that same place (i.e.,
still in p1)
while also being in one or more other sub-spaces of p1 (for
example, p3),
at the same time. In other words, b could be in p1, and
while not in all of p1 (i.e., not in,
say, p2,
which is a proper part of p1),
it would still be inp1
(in this case, in, say, p3,
which is also a proper part of p1).

Hence, b could be in p1 at t, but not in
every part ofp1 at t
-- and either be in motion or stationary, at that time --, meaning that b
would be in two places at once: p1 and p3.
So, if the location of bodies can be given in finer-grained detail -- even if
this manoeuvre is inconsistently disallowed of time -- a body could still be in one place and not in
it, and be in two places at once, while being stationary, with no contradiction
implied.

[This is the simplest of these cases; the reader is left to
determine more complicated examples for herself. The
complex nature of ordinary and/or
technical language allows for the depiction of motion and location in ways undreamt of by
Zeno, Heraclitus,
and Hegel -- or even Engels -- that is, in their 'philosophical'
deliberations. On this, see below and in the main body
of this Essay.]

Some might think this ignores what Engels
actually says:

"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Engels
(1976), p.152.
Bold emphasis added.]

However, as we saw earlier, it is far from clear what Engels meant by the
following:

"...even simple mechanical change of place can only come
about through a body being both in one place and in another place at one and the
same moment of time, being in one and the same
place and also not in it." [Ibid.]

Here, Engels says that a moving object is "in one and the same
place and not in it." He is clearly using "in" in a rather odd way, and it isn't too
clear whether he (or any other dialectician) is capable of explaining how this
could be literally true -- save they just label it a 'contradiction',
take their bat and ball home, and then retreat into a dialectical sulk. But,
that just highlights the problem: this DM-response doesn't make it any
easier to determine what Engels is proposing, or if he is proposing anything
determinate at
all.

In that case, it is worth pointing out that in L13:

L13: For some b, for just one instant t, for
three places p1, p2 and p3,
b is at p1 at t, but not at p2
at t, and b is at p3 at t, where p2
and p3 are proper parts of p1,

in this case: b is in
p1and not in it in the following sense: it is in p1
but not in all of p1
at the same time. This is just as legitimate an interpretation of Engels's words as the traditional
(but hopelessly obscure) version is.

This analysis might be contested on the grounds that
it simplyremoves the
contradiction from Engels's analysis.

But, and despite what he himself says, it isn't too clear that Engels's
words were contradictory to begin with, since little sense can be made of them
as they stand. If we can form no clear idea what Engels was trying to say,
then based on what he did say about motion it can't
justifiably be concluded that it is "contradictory".

"Motion itself is a contradiction; even simple mechanical
change of place can only come about through a body being both in one place
and in another place at one and the same moment of time, being in one and the same
place and also not in it." [Ibid. Bold emphasis added.]

We have already seen that extended bodies
can be in two places at
the same time -- even while they are stationary -- with no contradiction implied,
so the allegedly contradictory aspect of motion must arise from the following clause:

"...being in one and the same
place and also not in it [at the same moment in time -- RL]."

Well, is this the contradiction we have been led to
all along to accept?

If so, imagine the following scenarios:

[1]
NN is queuing for tickets, and finds herself at the front of the queue at
11:55am (before the Ticket Office opened at noon), but she needs to leave the
queue to
get something to eat. So, she asks MM to act as her proxy in the queue while she
goes off to buy some sandwiches, which she does at 11.57am. Here, NN is both in and not in the queue
at 11:57. She is still in the queue since MM is guarding her place, but
she isn't in the queue since she has left to get food. Here we have a moving
body, NN, who is both in the queue and not in it at the same time, with no
contradiction implied -- i.e., this only appears contradictory because of the equivocal
meaning of "in", here.

[2]
NM is selected by his coach to play for the first team squad.
The team leaves for a match at 15:00 hours, but NM misses the plane. So,
NM is in
the team (the coach hasn't dropped him), but not in the team (he isn't
accompanying them), all at the same time -- and this could be true
whether or not NM is moving. [Some might want to point out that a team is not a
place, but quite apart from the fact that Engels was unclear what he meant by
"place", we often speak about a player securing or gaining their place in the
team.] Here, once again, the equivocation centres on "in" and "place".

Let an object slide down the central tube that runs through this
bottle. Now, because the inside of this bottle is the same as the outside, that object will be inside and not inside this bottle at the same moment; it would
be in and not in the same place at once. And, this would be so whether or not the said
object was moving. [Here, the equivocation centres on "same place", i.e.,
whether "inside" can be the same as "outside" in certain circumstances. A
similar ambiguity also features in example [5], below.]

[An analogous 'contradiction' can be manufactured for a stationary
object on the surface of a
Möbius Strip
--
or even worse, on a set of
Möbius
Gears:

Figure Six: A Möbius Strip -- Concocted By
The CIA?

Figure Seven: Möbius Gears -- A CIA Invention?

Video Two: As If To Rub It In -- Möbius Gears

In Action

[See also
here. A stationary object
on these gears would be on top and not on top of one surface all at once. Here we can see
that equivocations like this aren't confined to the preposition "in".]

[4]
MN has had her amputated hand replaced by a
prosthetic.
At 02.20pm she inserts this artificial hand into a glove. Hence, her hand is
both in and not in that glove. Her hand is in the glove in the sense that this is her hand now.
But, it isn't in the glove in
the sense that it isn't a real hand, or the hand she was born with. [Here the equivocation
concerns "same object".]

[5]
NN is in the corridor of a hotel outside her room at 17:30
hours (on a Friday), but at the same time she is inside the hotel. So, she is
outside and inside (or outside and not outside), all at once. There are
countless examples of this use of prepositions and adjectives. For example, a
book on a shelf may be above the floor but below the roof. So, it is at one and
the same time above and not above. A box might be stored near a wall but far
from the door; so, at one and the same time, it is both near and not near. [Ancient Greek
Philosophers made much of these equivocations.] So, here we have an apparent
contradiction even though the items in question can be stationary with respect
to some inertial frame.

It might be objected that not only are these examples
artificial and forced, they are not at all what Engels had in mind.

But,
as we have seen, it isn't at all clear
what Engels meant. Anyway, only [3] is even arguably artificial.

That isn't the case with the following
example:

Here is a sports story from the BBC (concerning the 3000 metre
steeplechase final at the 2014 European Games):

"France's Mahiedine Mekhissi-Benabbad has been stripped of
his 3,000m steeplechase gold medal at the European Championships for taking his
shirt off on the home straight. Mekhissi-Benabbad put his top in his mouth after
pulling clear of the field. Initially he appeared to be shown a yellow card by
an official but was subsequently disqualified. Frenchman Yoann Kowal now wins
gold, Poland's Krystian Zalewski gets silver and Spain's Angel Mullera wins
bronze." [Quoted from
here.
Accessed 15/08/2014. Paragraphs merged to save space.]

As a result, Yoann Kowal was moved from second to first,
Krystian Zalewski from third to second, and Angel Mullera from fourth to third,
even while none of them were in two places at once, in one and not in it at
the same time. So, the Olympic officials moved and did not move Yoann Kowal; he is and isn't the winner
of the Gold Medal at these Games; he is both in and not in first place. Is
anyone taken in, or even puzzled by, these 'contradictions'?

Moreover, the examples given in [5] aren't artificial,
either;
indeed, there are countless instances of this sort of equivocation right across
the planet (nay, right across the universe) every day of the week:
Pluto is both
near the Earth (compared to its shortest distance from Proxima
Centauri), and far from the Earth (compared
to its shortest distance from
Neptune) --
hence, Pluto is both near and not near the Earth. Does anyone in their left mind
think this is a contradiction?

And, as we will discover, in the abstract, while Engels's 'theory'
might seem (to some) to be eminently sound, when we look at concrete examples
(like those above, or even those below), it can be seen for what it is: artificial and
forced itself.

For more examples like this, and worse, see Note 15,
Note 16, as well as the main body of this
Essay.

14a. It could be
objected that
(X1, Y1, Z1)
in this example is a mathematical point. If so, it can't have other
points located inside of it -- so it can't be the case that: "(X3, Y3, Z3)
and
(X2, Y2, Z2) are both located inside
(X1, Y1, Z1)."

That is easily rectified:

L13c: A stationary body, b, observed over the course of
an instant, is located in a finite region,ℛ, and
at (X3, Y3, Z3), but not at
(X2, Y2, Z2), where (X3, Y3, Z3)
and
(X2, Y2, Z2)
are both located inside ℛ.

L13d: A moving body, b, observed over the course of
an instant, is located in a finite region,ℛ, and
at (X3, Y3, Z3), but not at
(X2, Y2, Z2), where (X3, Y3, Z3)
and
(X2, Y2, Z2)
are both located inside ℛ.

14b. It could be
argued that the ship example is ridiculous since the places occupied by the ship
don't lie along the same line. Engels comments about motion clearly imply that a
moving body will do so along a given trajectory; it won't be all over the place
as the ship homily suggests. That objection has been batted out of the park in
Note 15, where the ship example has been translated into vector algebra.
Less technically, we need only add an additional codicil to the example given in
the main body of this Essay that the parts of the aforementioned port mentioned
in that example all lie along a straight line.

15. The following is an example of this type of motion partially expressed in vector
algebra:

V1: Let B be a body moving in
ℝ3
(or some Vector Space) with
respect to a given reference frame.